Concept in UK law
In English law, natural justice is technical terminology for the rule against bias ("nemo iudex in causa sua") and the right to a fair hearing ("audi alteram partem"). While the term "natural justice" is often retained as a general concept, it has largely been replaced and extended by the general "duty to act fairly".
The basis for the rule against bias is the need to maintain public confidence in the legal system. Bias can take the form of actual bias, imputed bias, or apparent bias. Actual bias is very difficult to prove in practice whereas imputed bias, once shown, will result in a decision being void without the need for any investigation into the likelihood or suspicion of bias. Cases from different jurisdictions currently apply two tests for apparent bias: the "reasonable suspicion of bias" test and the "real likelihood of bias" test. One view that has been taken is that the differences between these two tests are largely semantic and that they operate similarly.
The right to a fair hearing requires that individuals should not be penalized by decisions affecting their rights or legitimate expectations unless they have been given prior notice of the case, a fair opportunity to answer it, and the opportunity to present their own case. The mere fact that a decision affects rights or interests is sufficient to subject the decision to the procedures required by natural justice. In Europe, the right to a fair hearing is guaranteed by Article 6(1) of the European Convention on Human Rights, which is said to complement the common law rather than replace it.
Background.
Natural justice is a term of art that denotes specific procedural rights in the English legal system and the systems of other nations based on it. It is similar to the American concepts of fair procedure and procedural due process, the latter having roots that to some degree parallel the origins of natural justice.
Although natural justice has an impressive ancestry and is said to express the close relationship between the common law and moral principles, the use of the term today is not to be confused with the "natural law" of the Canonists, the mediaeval philosophers' visions of an "ideal pattern of society" or the "natural rights" philosophy of the 18th century. Whilst the term "natural justice" is often retained as a general concept, in jurisdictions such as Australia,583 and the United Kingdom,320 it has largely been replaced and extended by the more general "duty to act fairly". Natural justice is identified with the two constituents of a fair hearing,322 which are the rule against bias ("nemo iudex in causa sua", or "no man a judge in his own cause"), and the right to a fair hearing ("audi alteram partem", or "hear the other side").
The requirements of natural justice or a duty to act fairly depend on the context. In "Baker v Canada (Minister of Citizenship and Immigration)" (1999), the Supreme Court of Canada set out a list of non-exhaustive factors that would influence the content of the duty of fairness, including the nature of the decision being made and the process followed in making it, the statutory scheme under which the decision-maker operates, the importance of the decision to the person challenging it, the person's legitimate expectations, and the choice of procedure made by the decision-maker. 
Earlier, in "Knight v Indian Head School Division No 19" (1990), the Supreme Court held that public authorities which make decisions of a legislative and general nature do not have a duty to act fairly, while those that carry out acts of a more administrative and specific nature do. Preliminary decisions will generally not trigger the duty to act fairly, but decisions of a more final nature may have such an effect. 
Whether a duty to act fairly applies depends on the relationship between the public authority and the individual. No duty exists where the relationship is one of master and servant, or where the individual holds office at the pleasure of the authority. On the other hand, a duty to act fairly exists where the individual cannot be removed from office except for cause. Finally, a right to procedural fairness only exists when an authority's decision is significant and has an important impact on the individual.
Rule against bias.
In general.
People are barred from deciding any case in which bias exists or bias may fairly be suspected. This principle embodies the basic concept of impartiality, and applies to courts of law, tribunals, arbitrators and all those having the duty to act judicially. A public authority has a duty to act judicially whenever it makes decisions that affect people's rights or interests, and not only when it applies some judicial-type procedure in arriving at decisions.
The basis on which impartiality operates is the need to maintain public confidence in the legal system. The erosion of public confidence undermines the nobility of the legal system and leads to ensuing chaos. The essence of the need for impartiality was observed by Lord Denning, the Master of the Rolls, in "Metropolitan Properties Co (FGC) Ltd v Lannon" (1968): "Justice must be rooted in confidence and confidence is destroyed when right-minded people go away thinking: 'The judge was biased.'"599
Public confidence as the basis for the rule against bias is also embodied in the often-quoted words of Lord Hewart, the Lord Chief Justice of England and Wales, that "[i]t is not merely of some importance, but of fundamental importance that justice should not only be done, but should manifestly be seen to be done".
Forms of bias.
Actual and imputed bias.
Bias may be actual, imputed or apparent. Actual bias is established where it is actually established that a decision-maker was prejudiced in favour of or against a party. However, in practice, the making of such an allegation is rare as it is very hard to prove.
One form of imputed bias is based on the decision-maker being a party to a suit, or having a pecuniary or proprietary interest in the outcome of the decision. Once this fact has been established, the bias is irrebuttable and disqualification is automatic—the decision-maker will be barred from adjudicating the matter without the need for any investigation into the likelihood or suspicion of bias. A classic case is "Dimes v Grand Junction Canal" (1852), which involved an action between Dimes, a local landowner, and the proprietors of the Grand Junction Canal, in which the Lord Chancellor, Lord Cottenham, had affirmed decrees made to the proprietors. However, it was discovered by Dimes that Lord Cottenham, in fact, owned several pounds' worth of shares in the Grand Junction Canal. This eventually led to the judge being disqualified from deciding the case. There was no inquiry as to whether a reasonable person would consider Lord Cottenham to be biased, or as to the circumstances which led Lord Cottenham to hear the case.
In certain limited situations, bias can also be imputed when the decision-maker's interest in the decision is not pecuniary but personal. This was established in the unprecedented case of "R v Bow Street Metropolitan Stipendiary Magistrate Ex parte Pinochet Ugarte (No.2)" (1999). In an appeal to the House of Lords, the Crown Prosecution Service sought to overturn a quashing order made by the Divisional Court regarding extradition warrants made against the ex-Chilean dictator, Senator Augusto Pinochet. Amnesty International (AI) was given leave to intervene in the proceedings. However, one of the judges of the case, Lord Hoffmann, was a director and chairperson of Amnesty International Charity Ltd. (AICL), a company under the control of AI. He was eventually disqualified from the case and the outcome of the proceedings set aside. 
The House of Lords held that the close connection between AICL and AI presented Lord Hoffmann with an interest in the outcome of the litigation. Even though it was non-pecuniary, the Law Lords took the view that the interest was sufficient to warrant Lord Hoffmann's automatic disqualification from hearing the case. In "Locabail (UK) Ltd v Bayfield Properties Ltd" (1999), the Court of Appeal warned against any further extension of the automatic disqualification rule, "unless plainly required to give effect to the important underlying principles upon which the rule is based".465
Apparent bias.
Apparent bias is present where a judge or other decision-maker is not a party to a matter and does not have an interest in its outcome, but through his or her conduct or behaviour gives rise to a suspicion that he or she is not impartial. An issue that has arisen is the degree of suspicion which would provide the grounds on which a decision should be set aside for apparent bias. Currently, cases from various jurisdictions apply two different tests: "real likelihood of bias" and "reasonable suspicion of bias".
The real likelihood test centres on whether the facts, as assessed by the court, give rise to a real likelihood of bias. In "R v Gough" (1993), the House of Lords chose to state the test in terms of a "real danger of bias", and emphasized that the test was concerned with the possibility, not probability, of bias. Lord Goff of Chievely also stated that "the court should look at the matter through the eyes of a reasonable man, because the court in cases such as these personifies the reasonable man".670 However, the test in "Gough" has been disapproved of in some Commonwealth jurisdictions. One criticism is that the emphasis on the court's view of the facts gives insufficient emphasis to the perception of the public. These criticisms were addressed by the House of Lords in "Porter v Magill" (2001). The Court adjusted the "Gough" test by stating it to be "whether the fair-minded and informed observer, having considered the facts, would conclude that there was a real possibility that the tribunal was biased".494 This case therefore established the current test in the UK to be one of a "real possibility of bias".
On the other hand, the reasonable suspicion test asks whether a reasonable and fair-minded person sitting in court and knowing all the relevant facts would have a reasonable suspicion that a fair trial for the litigant is not possible. Although not currently adopted in the UK, this test has been endorsed by the Singapore courts.
It has been suggested that the differences between the two tests are largely semantic and that the two tests operate similarly. In "Locabail", the judges stated that in a large proportion of the cases, application of the two tests would lead to the same outcome. It was also held that "[p]rovided that the court, personifying the reasonable man, takes an approach which is based on broad common sense, and without inappropriate reliance on special knowledge, the minutiae of court procedure or other matters outside the ken of the ordinary, reasonably well-informed members of the public, there should be no risk that the courts will not ensure both that justice is done and that it is perceived by the public to be done".477 
In the Singapore High Court decision "Tang Kin Hwa v. Traditional Chinese Medicine Practitioners Board" (2005), Judicial Commissioner Andrew Phang observed that the real likelihood test is in reality similar to that of reasonable suspicion. First, "likelihood" is in fact "possibility", as opposed to the higher standard of proof centring on "probability". Secondly, he suggested that "real" in "real likelihood" cannot be taken to mean "actual", as this test relates to apparent and not actual bias. He also observed that both the court's and the public's perspectives are "integral parts of a holistic process" with no need to draw a sharp distinction between them.617–8
In contrast, in "Re Shankar Alan s/o Anant Kulkarni" (2006), Judicial Commissioner Sundaresh Menon thought that there was a real difference between the reasonable suspicion and real likelihood tests.101 In his opinion, "suspicion" suggests a belief that something that may not be provable could still be possible. "Reasonable" suggests that the belief cannot be fanciful. Here the issue is whether it is reasonable for the one to harbour the suspicions in the circumstances even though the suspicious behaviour could be innocent. On the other hand, "likelihood" points towards something being likely, and "real" suggests that this must be substantial rather than imagined. Here, then, the inquiry is directed more towards the actor than the observer. The issue is the degree to which a particular event is not likely or possible99 Menon J.C.