Conservative Party co-treasurer Peter Cruddas has resigned after secretly filmed footage showed him apparently offering access to the prime minister for a donation of £250,000 a year.
He made the claim toSunday Timesreporters posing as potential donors.
He said £250,000 gave "premier league" access, including dinner with David Cameron and possibly the chance to influence government policy.
Mr Cameron said the claim was "completely unacceptable".
Speaking at a Sports Relief run in Buckinghamshire, which he was taking part in, the prime minister said: "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."
The Sunday Times said the fake company was a wealth fund based in Liechtenstein.
Donations from it would have been ineligible under electoral law, but not from British company directors who were registered on the UK electoral roll, the reporters were told by a lobbyist they hired, Sarah Southern.
In the footage, Mr Cruddas is heard initially saying that it was not possible to buy access to the prime minister.
But he then goes on to discuss what access different size donations would get.
He spoke about the Leader's Group,a club where for an annual donation of £50,000 donors are invited to join Mr Cameronand other senior figures from the Conservative Party at dinners, post-Prime Minister's Questions lunches, drinks receptions, election result events and important campaign launches.
However, he said more money would allow more access, including to Chancellor George Osborne.
"Two hundred grand to 250 is premier league… what you would get is, when we talk about your donations the first thing we want to do is get you at the Cameron/Osborne dinners," he says.
He said the meetings were good for picking up "a lot of information", and that he would ensure suggestions were fed back to No 10.
"You will be able to ask him [Mr Cameron] practically any question you want.
"If you're unhappy about something, we will listen to you and put it into the policy committee at Number 10 - we feed all feedback to the policy committee."
Mr Cruddas was appointed Tory co-treasurer in June 2011. Lord Fink will return as principal treasurer, the party announced on Sunday morning, with Michael Farmer acting as co-treasurer.
Resigning, Mr Cruddas said: "I deeply regret any impression of impropriety arising from my bluster in that conversation."
He said he had had an "initial conversation" with the reporters and no further action was taken by the party.
"Clearly there is no question of donors being able to influence policy or gain undue access to politicians," he said.
"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."
He went on to say that in order to make this position "clear beyond doubt" he had decided to resign.
A statement from the Tories said: "No donation was ever accepted or even formally considered by the Conservative Party.
"All donations to the Conservative Party have to comply with requirements of electoral law, and these are strictly enforced by our compliance department."
Downing Street sources said: "He was saying numerous things no-one recognised."
They also stressed that there was no policy committee at No 10.
Labour said it wanted the names of Tory donors who have visited government property - including Downing Street and Chequers - and of those who have made submissions to the Downing Street policy unit, to be published.
Labour deputy chairman Tom Watson said: "It's David Cameron that hosts the dinner parties, and people would expect him to explain how - when people have given a quarter of a million pounds - how those dinner parties are held."
Labour MP David Miliband said: "The idea that policy is for sale is grotesque.
"This goes to the heart of the question of the relationship between a party and the government... It crashes through the lines that should exist between party and government."
Coalition partners the Liberal Democrats were also concerned. Lib Dem MP Danny Alexander said: "It's utterly disgraceful and there is no place for this sort of unacceptable behaviour in British politics."
He also said "reform" of funding system was necessary.
He said there was a "perception that people who make large donations - be they wealthy people from the city or trade unions - have influence. They should not have that influence, nor the perception of that influence."
Last year, after an inquiry into public funding of political parties, the Committee for Standards in Public Life said political parties should get an extra £23m of taxpayers' money to reduce reliance on "big money" donations.
It also recommended a £10,000 annual cap on individual donations from 2015.
At present there are no limits on donations, but the name of anyone who gives more than £7,500 to a party is made public.
Committee chairman Sir Christopher Kelly said on Sunday that events like this were "absolutely inevitable".
"This sort of thing will happen as long as the parties depend on wealthy individuals for their existence," he told the BBC.
He said he had recommended that "the only way to remove the suspicion surrounding very large donations would be to ban very large donations".
"That requires all the parties to address something very hard. For the Conservatives it means giving up their advantage of having more wealthy supporters. For Labour, the relationship with the trade unions," he said.