The Archbishop of Canterbury has attracted widespread criticism after appearing to back the adoption of some aspects of Sharia law in the UK.
Dr Rowan Williams said the UK had to "face up to the fact" some citizens did not relate to the UK legal system.
Culture Secretary Andy Burnham said such moves would create "social chaos."
But Bishop of Hulme, the Rt Rev Stephen Lowe, criticised the "disgraceful" way in which the archbishop had been "ridiculed" and "lampooned" by some.
"We have probably one of the greatest and the brightest archbishops of Canterbury we have had for many a long day," he said.
The robust defence follows criticism of Dr Williams in some circles.
The BBC understands from sources who work on Christian-Muslim interfaith issues that the Dr Williams has faced a barrage of criticism from within the Church and has been genuinely taken aback by how his words were received.
Islamic Sharia law is a legal and social code designed to help Muslims live their daily lives, but it has proved controversial in the West for the extreme nature of some of its punishments.
Dr Rowan Williams told BBC Radio 4 on Thursday that he believed the adoption of some Sharia law in the UK seemed "unavoidable".
He said adopting parts of Islamic Sharia law could help social cohesion. For example, Muslims could choose to have marital disputes or financial matters dealt with in a Sharia court.
But Gordon Brown's spokesman said the prime minister "believes that British laws should be based on British values".
He added that Mr Brown had a good relationship with the archbishop, who was perfectly entitled to express his views.
Shaista Gohir, a government advisor on Muslim women and director of Muslim Voice UK, said she did not believe there was a need for Sharia courts because "the majority of Muslims do not want it".
Sharia law is Islam's legal system
It is derived from the Koran and the life of the prophet Mohammed
Sharia rulings help Muslims understand how they should lead their lives
A formal legal ruling is called a fatwa
In the West, Sharia courts deal mainly with family and business issues
English law recognises religious courts as a means of arbitration
She told BBC News: "Many Muslim commentators and the media are wrongly assuming that all Muslims want Sharia law in the UK.
"Various polls have so far indicated that around 40% want Sharia law. Although this is a significant percentage, why ignore the views of the other 60%?"
Following the archbishop's comments, Home Office Minister Tony McNulty said: "To ask us to fundamentally change the rule of law and to adopt Sharia law, I think, is fundamentally wrong."
Shadow community cohesion minister Baroness Warsi told BBC News 24: "Dr Williams seems to be suggesting that there should be two systems of law, running alongside each other, almost parallel, and for people to be offered the choice of opting into one or the other. That is unacceptable."
Liberal Democrat leader Nick Clegg said he had "an enormous amount of respect" for Dr Williams, but could not agree with him on this issue.
He said: "Equality before the law is part of the glue that binds our society together. We cannot have a situation where there is one law for one person and different laws for another."
Trevor Phillips, who chairs the Equality and Human Rights Commission, said the "implication that British courts should treat people differently based on their faith is divisive and dangerous".
In an interview with BBC correspondent Christopher Landau, Dr Williams said Muslims should not have to choose between "the stark alternatives of cultural loyalty or state loyalty".
He stressed "nobody in their right mind would want to see in this country the kind of inhumanity that's sometimes been associated with the practice of the law in some Islamic states; the extreme punishments, the attitudes to women as well".
'Respect and tolerance'
But Dr Williams said an approach to law which simply said "there's one law for everybody and that's all there is" was dangerous.
Under English law, people may devise their own way to settle a dispute in front of an agreed third party as long as both sides agree to the process.
HAVE YOUR SAY
There is, and should only be, one law which covers all people and to suggest it can be otherwise is to seriously damage our rights
Patricia London, UK
Muslim Sharia courts and Orthodox Jewish courts which already exist in the UK come into this category.
Dilwar Hussain of the Islamic Foundation, an influential think-tank on Muslims in Europe, said non-Muslims needed to be reassured that nobody wanted to invent a new legal system.
He said: "Most Muslims are perfectly happy with the legal system as it exists in the UK. They support it. It protects them, it includes provisions for Halal food and for banking services. In other words, some of the most important things that concern people are already there in the system.
"We are not seeking the introduction of a new system - absolutely not. But there are some areas, issues around families for example, where many Muslims would like to be able to find solutions according to what they believe. That is not incompatible with our law."
Ibrahim Mogra, of the Muslim Council of Britain, said: "We're looking at a very small aspect of Sharia for Muslim families when they choose to be governed with regards to their marriage, divorce, inheritance, custody of children and so forth.
"Let's debate this issue. It is very complex. It is not as straight forward as saying that we will have a system here."