David Cameron's revelation that he hosted private Downing Street meals for Tory donors has sparked calls for an independent inquiry into "cash for access" claims and urgent party funding reform.

The Prime Minister gave in to intense pressure to expose the meetings with wealthy benefactors after a co-treasurer of the party was caught promising meetings and influence in return for cash.

Labour dismissed an internal probe into Peter Cruddas - who has resigned - as a "whitewash" and said the issue should be investigated by the official adviser on ministerial interests.

As opinion polls suggested the Conservatives were losing support over the issue, senior party figures tried to turn attention instead to the wider question of political funding. Cross-party talks are expected to be reopened this week in a fresh bid to end the deadlock which has stymied attempts to reduce the influence of big donors for many years.

Mr Cruddas was caught on film telling undercover reporters that "premier league" gifts could secure meetings with ministers and influence policy. He quit his post on Saturday, hours after the Sunday Times revealed his comments.

After initially trying to brush off the controversy, the Tories released the names of donors - and their partners - who had been invited to the meals. There were 12 who had attended four dinners at Downing Street and five invited to informal lunches at official country residence Chequers since Mr Cameron's election in 2010. Labour said the super-rich business figures had donated more than £23 million since 2005.

Mr Cameron announced that eminent lawyer and Tory peer Lord Gold would conduct a party inquiry into the affair, and he said the party would in future release quarterly registers of significant donors invited to eat with him at official residences, as well as lists of those attending "Leader's Group" dinners for donors who give more than £50,000.

Former justice secretary Jack Straw has called on the Electoral Commission to investigate suggestions foreign donations could be channelled through a third party to escape rules outlawing overseas cash. Donations are only legal if they come from individuals on the electoral roll or from companies registered in the UK.

Sarah Southern, a former Conservative Party staffer now working as a lobbyist, was recorded by The Sunday Times saying: "The party will look at the criteria of which...in that document you'll have seen the kind of, the legal bullet points and as long as the money is coming from a legal UK registered donor, or a legal registered UK company that is operating then they'll normally be happy."

In a letter to the watchdog, Mr Straw wrote: "According to reports, undercover reporters told Mr Cruddas and Ms Southern that they were interested in making a donation on behalf of Middle Eastern donors. The reporters were allegedly told that money from foreign investors could be channelled through a company established by the reporters as they were on the UK electoral roll." He added: "These reports raise serious questions as to how the Conservative Party is soliciting donations, potentially in contravention of the Political Parties, Elections and Referendums Act 2000."