Conservative Party co-treasurer Peter Cruddas has resigned after being filmed apparently offering access to Prime Minister David Cameron in return for donations of £250,000 a year.
The senior Tory fundraiser told undercover reporters pretending to be business representatives that "things will open up for you" if they donated that amount of money to the Tories.
Announcing his resignation, Mr Cruddas said in a statement: "I deeply regret any impression of impropriety arising from my bluster in that conversation. Clearly there is no question of donors being able to influence policy or gain undue access to politicians.
"Specifically, it was categorically not the case that I could offer, or that David Cameron would consider, any access as a result of a donation. Similarly, I have never knowingly even met anyone from the Number 10 policy unit. But in order to make that clear beyond doubt, I have regrettably decided to resign with immediate effect."
On Sunday morning the Tories announced that Lord Fink is to replace Peter Cruddas as the party's principal treasurer.
Hedge fund millionaire Lord Fink previously held the role until earlier this month, when it was taken over by Mr Cruddas.
Speaking on Sunday morning David Cameron said: "What happened is completely unacceptable, this is not the way that we raise money in the Conservative party. It shouldn't have happened.
"I'll make sure there is a party inquiry to make sure this can't happen again."
A Tory spokesman said: "In the light of the resignation of Peter Cruddas yesterday, Lord Fink has agreed to return as the party's principal treasurer, the role he stepped down from at the beginning of March. Michael Farmer will continue to support Stanley Fink as a co-treasurer.
"We are grateful to Stanley for agreeing to this and we believe that this will ensure that the treasurers' department will continue to operate to the highest possible standards under his stewardship."
PETER CRUDDAS RESIGNATION - FULL COVERAGE
Mr Cruddas said he only took up the post at the beginning of the month and was "keen to meet anyone potentially interested in donating". He said he had not consulted any politicians or senior party officials before the recorded conversation.
Mr Cruddas told the undercover reporters that "premier league" donors - those giving £250,000 a year - could lobby Mr Cameron directly and their views were "fed in" to Downing Street. He said there was no point in "scratching around" with donations of £10,000.
According to The Sunday Times, he believed that any prospective donations from the reporters - pretending to be wealth fund executives - would come from Liechtenstein and would be ineligible under election law. They are said to have discussed the creation of a British subsidiary and the possibility of using UK employees to make the donation.
A Conservative Party spokesman said: "No donation was ever accepted or even formally considered by the Conservative Party. All donations to the Conservative Party have to comply with the requirements of electoral law.
"Unlike the Labour Party, where union donations are traded for party policies, donations to the Conservative Party do not buy party or government policy."
Labour challenged the Prime Minister to "come clean" about what he knew and when. "Time and again the Tory party has been the obstacle to capping donations from wealthy individuals. Now it appears obvious why," said Labour MP Michael Dugher who was speaking before Mr Cruddas quit.
The affair is likely to re-ignite the debate surrounding party funding, which has seen the Tories and Labour fail to reach a consensus despite both parties acknowledging the need for reform. The chairman of the Committee on Standards in Public Life, Sir Christopher Kelly, called last year for donations to be capped at £10,000 and for the parties to be funded largely by a taxpayer-funded grant.
But both parties dismissed the report, since the plan would curb the massive donations the unions pay to Labour and wealthy businessmen pump into Tory coffers.
Lib Dem Chief Secretary to the Treasury said the revelations were "utterly disgraceful."
"This makes the case for reforming the system of party funding even stronger," Alexander told the Andrew Marr Show on Sunday morning. "Over the next few weeks the three parties will be getting around the table.. to discuss how we can change how party funding works, to get the big funding out of politics."
Labour shadow minister Michael Dugher said:
"We now hear the Tory treasurer boasting that some of these same millionaires who got a tax cut in the Budget this week can buy a seat at the private Downing Street dinner parties of David Cameron and George Osborne through donations worth hundreds of pounds to the Conservative Party.
"Will the PM say exactly what he knew and when about an apparent effort to sell access and influence in Downing Street?"
Tory deputy chairman Michael Fallon said no donations to the party could ever influence its policies. "I think [Cruddas] was blustering and boasting. No donation was accepted.
"He made a mistake here, and he's resigned and he's been replaced... he over-boasted about what you could do with a particular donation. That was wrong. It would certainly not have got through our normal compliance checks.
"Businessmen of course, like anybody else.. get access to politicians all the time. That's part of the process of government, of listening to business. But the big change now is that if anyone meets a minister in the government, those meetings are not only recorded, but are published."