In an exclusive article for The Independent on Sunday on page 38, the controversial Labour supporter insisted that Jon Mendelsohn discussed Mr Abrahams's system of donating through intermediaries with him at a dinner in London, five months before Mr Mendelsohn became the Labour Party's head of election resources.
Mr Abrahams claims Mr Mendelsohn, a close ally of the Prime Minister, told him that the unconventional arrangement, which breaches electoral law, "sounds like a good idea".
Mr Mendelsohn last night dismissed Mr Abrahams's claims. He said: "This latest statement is fictional and completely untrue. I will be co-operating fully with the police in their investigation."
Labour's chief fundraiser has previously maintained that he had no knowledge of the proxy donations, totalling over 600,000, until he took over his new role in September, and queried a number of third-party donations with the former general secretary Peter Watt, who resigned over the affair last week.
But, in his first full account of his "social" encounter with the fundraiser during a British Board of Deputies dinner at which Gordon Brown was guest speaker, Mr Abrahams claimed financial support for Labour had been a central topic of conversation.
"I was placed next to Jon Mendelsohn which, at the time, I felt was just a little more than coincidence," he recalled, in a personal account which revealed his frustration at his treatment at the hands of rivals within and outside the Labour Party. "I then realised he was hoping to become Gordon Brown's fundraiser and he knew I was a strong supporter.
"He did not solicit funds from me at the dinner, however. I told him that I regularly donated to the party, and I described how it was done through intermediaries for the purposes of anonymity, to which he replied, 'That sounds like a good idea'."
The new attack on one of Mr Brown's closest confidants came as the third-party donors affair threatened to destabilise the Labour Party still further, with deputy leader Harriet Harman clinging on to her job amid revelations about how her campaign for the position had been financed.
Last Wednesday night Mr Abrahams said he had received a letter from Mr Mendelsohn, dated 24 November, asking to meet him next time he was in London. Mr Mendelsohn said he wrote to Mr Abrahams to arrange a meeting so he could inform him he was "unhappy" with the way he had disguised donations to the party. He said he was told by Mr Watt that these were disguised donations by Mr Abrahams, but were within the law. Mr Mendelsohn said he believed the donations "did not meet the strict transparency test that I wished to see in place" and wanted to meet Mr Abrahams to tell him the arrangement should end.
Mr Abrahams last night stressed that he had not believed he was breaking the law by failing to put his name to all 19 donations. But he pointed the finger at further, unnamed, senior Labour figures, who he claimed had been fully aware of the back channels through which he had been directing his contributions since they began in 2003.
Mr Abrahams said: "Party officials knew of my wish to retain my privacy and were only too happy to accept my money via intermediaries. Only a very few officials and party figures in the higher echelons of the national party structure were aware. Perhaps as a result I was received warmly at functions and was occasionally contacted to make further donations."
Mr Abrahams stepped up the pressure on Mr Mendelsohn by urging the fundraiser, who he said was one of "only a very few" people who knew about the proxy donations, to "stop damaging himself and the party's credibility".
In a separate statement, Mr Abrahams said: "He was one of only a very few people who were aware of this method of making donations to the party.
"He would be well advised now to stop damaging himself and the party's credibility. I will not stand by and allow my name to be put in the frame by spin doctors. The police must be allowed to conduct this inquiry free from the interference of politicians."
Details of Mr Abrahams's network of donations have plunged the party into renewed crisis only months after Labour was humiliated by the "cash-for-peerages" inquiry. The Electoral Commission passed a file on the affair to the Metropolitan Police on Friday, after it was confirmed that Scotland Yard had launched "Operation Minera", into "potential breaches" of the Political Parties, Elections and Referendums Act 2000.
Mr Brown has also asked former Labour general secretary Lord Whitty to carry out an internal investigation into the party's handling of the donations, which are to be handed back. The decision to return the "tainted" cash will now force the Labour leadership to take the begging bowl around union supporters in a bid to prevent a financial crisis.
Mr Abrahams's latest disclosures came as Mr Brown tried to fight back against the torrent of criticism that has dogged him since the affair came to light. The PM pledged yesterday to use the lessons of the embarrassing episode to push forward reform of the entire political party funding system. As he attempted to regain the initiative after a two-week battering, he called for a fresh consensus but warned he would not allow "one-party deadlock".
He told a meeting of Labour's National Policy Forum in west London: "The latest problems in party funding show why it is right not to delay but it is time to act. We have learned just how easily trust in our politics can be eroded. We must now complete the work of change, address the problems that still remain to be resolved, not hesitate to make the changes necessary and seek to build greater confidence in the integrity of our political system."
Mr Brown said reform proposals put forward by Sir Hayden Phillips, which include a 50,000 cap on individual donations, provided a "comprehensive framework for reform".
The Prime Minister appeared at the event alongside Harriet Harman, who was drawn into the donations controversy when it emerged she had accepted a 5,000 donation from one of Mr Abrahams's proxies. She said it had been a "very painful week for the party". The Prime Minister thanked Ms Harman "for what she said this morning and for what she does".
The Conservatives responded to the speech by accusing Mr Brown of trying to divert attention from Labour's woes.
The shadow Secretary of State for Work and Pensions, Chris Grayling, said: "This speech is a pretty opportunistic attempt by Gordon Brown to erect a smokescreen around events of the past two days.
"David Cameron wrote to him in October urging major reforms to party funding and a cap on donations. Gordon Brown refused because he didn't want to give up on the multimillion-pound financing from the trade unions. His decision to pick up the issue again today must be more than an attempt to divert attention away from party problems."
The acting Liberal Democrat leader, Vince Cable, said: "It is clear to everyone that if we are to have a fair and transparent party funding system then reform is needed urgently. Gordon Brown must now ensure that he does not lose sight of this fact in a desperate attempt to secure crude political advantage."
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