Labour have accused the Conservatives of trying to get round party funding rules with a 'secret' £1m-a-year call centre for Tory election candidates.
The party's old Smith Square HQ is at the centre of an investigation
The Tories have previously insisted the centre - run from a West Midlands manor house by a firm called Constituency Campaigning Services - was independent.
But David Cameron appeared to contradict this earlier, saying it was effectively part of the party.
The Tory leader's words prompted Labour calls for an urgent inquiry.
On Saturday, The Guardian reported that CCS gets £1m funding a year from the Midlands Industrial Council, a body which has been used by wealthy business people to donate almost £1m to the Conservatives without their identities being revealed.
The newspaper said the centre was being used to target key marginal constituencies ahead of the next general election.
In a statement, the Conservative Party said that CCS was a free-standing commercial organisation, independent of the Conservative Party, that provides printing, design and call centre services to some constituency associations".
It said the organisation was properly registered with the Electoral Commission as a "regulated donee", which entitles it to light touch regulation.
But Mr Cameron told BBC One's Sunday AM that Coleshill Manor was "effectively a part of the Conservative Party".
He also confirmed that he had met the members of the MIC, which he said was "an organisation that raises money from businesspeople".
He added: "Where those people are specifically giving money to the Conservative Party, they declare it in the right way."
A Labour source said that his comments appeared to indicate that the Tories had breached the Electoral Commission's rules, which state that membership associations registered as regulated donees cannot be part of a political party.
Work and Pensions Secretary Mr Hutton said: "These stunning admissions by David Cameron raise serious questions about the Tories' secret funding arrangements."
Mr Hutton added that Mr Cameron had confirmed he met members of the Midlands Industrial Council, "through which businessmen have given hundreds of thousands of pounds to the Tories in complete anonymity.
"If David Cameron's pledge to 'clean up politics' is to have any credibility he now needs to name these secret backers who are bankrolling Tory campaigns while hiding behind the Midlands Industrial Council."
The Electoral Commission said that CCS - following a recent flotation - was now "owned by the party" but no longer "part of the party".
A spokeswoman said the commission was looking into the status of MIC and had been supplied with fresh information about the organisation by the party a few days ago.
It was standard practice to ask for such details, a spokeswoman said, insisting it had not launched any formal inquiry into the controversy.
In a separate development, the Conservative Party has told The Sunday Telegraph it does not know who sold it two Westminster properties in a deal being investigated by the Electoral Commission.
The party bought the freehold of its former headquarters in Smith Square, the paper reports, and a second property in nearby Tufton Street in March by acquiring Platinum Overseas Holdings, an offshore company based in the British Virgin Islands.
The party is attempting to sell the properties for £30m for a profit alleged by its critics of £4.35m.
The Liberal Democrats claim whoever sold Platinum to the Conservatives did so at £4.35m less than its market value, which would constitute an anonymous donation.
But Tory chairman Francis Maude told The Sunday Telegraph he did not know who the owners of Platinum were, as the sale had been conducted by US investment bankers Citigroup.
Mr Maude has denied the deal amounts to a "hidden donation", insisting it was a commercial transaction.
The Electoral Commission is investigating the circumstances surrounding the Platinum sale.