The man heading up the cash-for-honours inquiry, Assistant Commissioner John Yates, is focusing on whether two pieces of legislation were breached. But what do the laws actually say?
1925 HONOURS (PREVENTION OF ABUSES) ACT
It is a law designed to deal with those who both give and accept honours under inducement.
It was introduced after a scandal in the early 1920s, when David Lloyd
George offered peerages and other honours at a price.
The money was
supposed to go to Liberal Party funds, but in fact most of it found its way into
Lloyd George's own pocket.
As one contemporary wrote: "Anyone could buy a barony for £50,000, a
baronetcy for £25,000, or a knighthood for £15,000."
The scandal did not immediately become public
knowledge because Lloyd George also conferred titles on newspaper owners,
to ensure their silence.
By 1925, the situation had got so out of hand that Parliament decided to introduce
Anyone found guilty under the Act could face imprisonment for up to two years or an unlimited fine.
But it has brought only one conviction, for selling honours, in a 1933 case involving Maundy Gregory, a man who had close connections with Number 10.
Section One of the Act says this: "If any person accepts, obtains or agrees
to accept or obtain from any person, for himself or for any other person, or for
any purpose, any gift, money or valuable consideration as an inducement or
reward for procuring or assisting or endeavouring to procure the grant of a
dignity or title of honour to any person or otherwise in connection with such a
grant, he shall be guilty of a misdemeanour."
Political Honours Scrutiny Committee of privy councillors, set up to weed out
unsuitable nominees was also a result of the Lloyd George scandal.
POLITICAL PARTIES, ELECTIONS AND REFERENDUMS ACT 2000
The police investigation began into possible breaches of the 1925 Act, but officers said it quickly became clear there were "inevitable overlaps" with the more recent PPER act.
This law, which came into force in 2001, implemented recommendations made by the Neill Committee, set up by the government to look into the way political parties received money.
In part it was a response to the sleaze allegations which dogged the previous Conservative government, such as the "cash for questions" scandal, which effectively ended the political career of MP Neil Hamilton.
But Labour faced its own controversy after accepting a £1m loan from Formula 1 boss Bernie Ecclestone, then later exempting F1 from a ban on sports sponsorship by tobacco companies.
The money was repaid to avoid accusations it had been used to "buy" policies.
The PPER Act forced political parties to declare publicly donations of more than £5,000, banned foreign donations and put a cap on election spending.
If the loans given to political parties really turned out to be concealed donations, which should have been declared, then the law would be broken.
Inquiries are focusing on whether loans were given at genuine commercial rates.
But defining what exactly a commercial rate is may prove difficult - the Electoral Commission, which enforces the Act, provides some guidelines but no strict definition.
PERVERTING THE COURSE OF JUSTICE
During the course of the investigation, the police have also asked questions about perverting the course of justice and conspiracy to pervert the course of justice.
Tony Blair's aide Ruth Turner was arrested on suspicion of offences under the Honours (Prevention of Abuses) Act but was also questioned on suspicion of perverting the course of justice. She was released on police bail and has not been charged.
Fundraiser Lord Levy was questioned on 30 January on suspicion of conspiracy to pervert the course of justice, the second time he has been arrested, but was also not charged.
The offence of perverting the course of justice is committed if someone does something which perverts - or was intended to pervert - the course of public justice.
Any charge of perverting the course of justice would be an offence under common law, and carried a theoretical maximum sentence of life in prison. However, no sentence longer than 10 years has ever been handed down.