The Liberal Democrats have formally urged the police to investigate apparent "serious breaches" of party funding laws by Labour.
Acting leader Vincent Cable said it was essential to "establish the facts" and press charges if necessary.
Lib Dem leadership hopeful Chris Huhne has written to Met Police boss Sir Ian Blair asking him to investigate.
Gordon Brown has said donations made to Labour through intermediaries were unlawful and has announced an inquiry.
But, asked in prime minister's questions earlier why he had not called in the police, he said he had followed convention in referring the matter to the Electoral Commission.
The commission has begun its own inquiry and Mr Brown has asked Labour veteran Lord Whitty to hold an internal inquiry.
Mr Abrahams gave £663,975 to Labour, but under four other people's names.
In a statement, Mr Cable said: "At first sight it appears that there may have been serious breaches of the law in relation to senior figures in the Labour Party accepting proxy donations from David Abrahams.
"It is essential to establish the facts in this case, and for anyone who has broken the law to take the consequences for their actions."
He said the police should investigate "fully" and the Crown Prosecution Service should decide if anyone should be charged.
The Metropolitan Police has recently finished a lengthy, £1.4m inquiry - prompted by the Scottish nationalist MP Angus MacNeil's complaint - into allegations that honours were given in return for cash.
That inquiry, which cast a shadow over Tony Blair's final months as prime minister, ended with no charges being brought.
Earlier Mr Huhne, who is battling with Nick Clegg to become the Lib Dems' next leader, said there were "conflicts of interest" in the inquiries announced by Mr Brown. He pointed out that Lord McCluskey had been a solicitor general in Harold Wilson's government.
"Frankly we do need a police inquiry. We need to clear the air and get the police involved," he told the BBC's Daily Politics.
A Metropolitan Police spokeswoman said the force had not yet received Mr Huhne's letter, nor had the Electoral Commission requested that it investigate Mr Abraham's donations.
Mr MacNeil said he had not written to the police this time as he believed the commission was taking it seriously.
But he challenged Mr Huhne or Mr Clegg to "lead by example" and commit to repaying the £2.4m donation their party received from Michael Brown in 2005.
The following year, Mr Brown was jailed for perjury.