Conservative Party co-treasurer Peter Cruddas resigns after being filmed boasting that people willing to donate £250,000 would gain access to the prime minister and the Downing Street policy unit.
Journalists from the Sunday Times posed as wealth fund executives to record the meeting with Mr Cruddas.
He told them that "premier league" Tory donors - those giving £250,000 a year - could lobby Mr Cameron directly and their views would be "fed in" to the Downing Street policy unit.
Conservative donors who pay more than £50,000 a year already get personal access to the Prime Minister via the "Leader's Group". But the party insists that there is no question of donors' views influencing government policy.
'Things will open up'
Mr Cruddas was caught on camera boasting that "things will open up" for anybody willing to donate £250,000 a year. He told the undercover journalists there was no point in "scratching around" with donations of £10,000.
According to The Sunday Times, he believed that any prospective donations would come from Liechtenstein and would be ineligible under election law.
But he is said to have discussed the creation of a British subsidiary and the possibility of using UK employees to make the donation, adding: "It will be awesome for your business."
The journalists secured the two-hour meeting with Mr Cruddas through Sarah Southern, a former Conservative Party staffer now working as a lobbyist. The Sunday Times said she told the reporters they should make a "huge donation" if they wanted access to senior government figures.
Apology for 'bluster'
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."
The Conservatives have announced that Lord Fink will return as the party's main treasurer, just weeks after he handed over the reins to Mr Cruddas.
Lord Fink and his fellow co-treasurer Michael Farmer are both City financiers and have made donations to the Conservatives that make them eligible for membership of the Leader's Group - a club for major backers.
According to the Conservative Party website, members of the Group "are invited to join David Cameron and other senior figures from the Conservative Party at dinners, post-PMQ lunches, drinks receptions, election result events and important campaign launches".
A spokesman for the party said: "All donations to the Conservative Party have to comply with the requirements of electoral law. These are strictly enforced by our compliance department.
"Unlike the Labour Party, where union donations are traded for party policies, donations to the Conservative Party do not buy party or government policy."
Union leader Bob Crow, general secretary of the RMT, said: "This morning's revelations expose the sleaze and hypocrisy at the heart of the Tory party in all its gory detail.
"Those same people who attack the open and democratic finances and structures of the trade unions caught up to their necks in another cash for access scandal."
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Cameron promises inquiry
Mr Cameron told BBC News: "What happened is completely unacceptable. This is not the way that we raise money in the Conservative Party, it shouldn't have happened."
"It's quite right that Peter Cruddas has resigned. I will make sure there is a proper party inquiry to make sure this can't happen again."
Liberal Democrat Chief Secretary to the Treasury Danny Alexander said Mr Cruddas's comments were "utterly disgraceful" and made the case again for reform of party funding - an issue that came under scrutiny when Tony Blair's government was embroiled in allegations that honours were awarded in return for cash for the Labour Party. Attempts at a cross-party consensus for reform have repeatedly foundered.
Sir Christopher Kelly, chairman of the independent Committee on Standards in Public Life, warned today that the parties could "duck the issue no longer".
He added: "It would be wrong to regard this as an isolated event. Events like it are inevitable as long as the main political parties are dependent for their existence on large donations from rich individuals or, in the case of the Labour Party, a small number of trade unions.
"The parties collectively need urgently to address the damage this does to confidence in the integrity of the political process.
Mr Miliband, the former foreign secretary, urged Mr Cameron to publish a list of policies that had been passed on to the Prime Minister and Downing Street from donors attending dinners and other events.
"I would say he should do that now, because this goes to the heart of the relationship between a party and a government," he told BBC1's Andrew Marr Show.
"It blurs the lines - in fact it crashes through the lines - that should exist between party and government."