Labour has denied that Mr Miliband avoided tax through the arrangement, pointing out that the party leader paid capital gains tax on his share of the north London property when he later sold it to his brother David.
But Tory MP Andrew Bridgen described the denial as “risible”, claiming that the arrangement - known as a deed of variation - had initially been set up to avoid possible future inheritance tax liabilities.
Mr Miliband has confirmed that his mother Marion set up an arrangement known as a deed of variation after the death of his father Ralph, which is understood to have allowed ownership of the property to be split between Mrs Miliband and her sons.
However, Mr Miliband has since sold his share to his brother David, who also bought the remainder of the property from his mother. As Mrs Miliband is still living and is no longer the owner of the property, no inheritance tax liability has arisen.
A Labour spokesman said Mr Miliband paid capital gains tax at 40% on the sale and said any suggestion that he used the arrangement to avoid tax would be a “straightforward lie”.
The spokesman said: “Ed paid 40 per cent capital gains tax when the house was sold in 2004/05. It can’t be tax avoidance if no tax was avoided.”
But Mr Bridgen said: “This is weak and risible from Ed Miliband, who is desperately trying to wriggle out of his previous efforts to avoid inheritance tax.
“Here are the facts: It is absolutely beyond doubt - and not for a moment denied by Ed Miliband - that he and his family used a deed of variation in 1994 and that this arrangement was in place for 10 years. As the former head of tax at PwC has said ‘the reason people use deeds of variation is to save on inheritance tax’.
“Ed Miliband should now publish this deed of variation that he is currently hiding away and be as open about his own tax affairs as he demands others to be. The public can then judge for themselves.”
Mr Miliband has gone on the attack in recent days over allegations of tax avoidance activities linked to some wealthy supporters of the Conservative Party, telling the House of Commons that David Cameron was “a dodgy Prime Minister surrounded by dodgy donors”.
He yesterday accused the Conservatives of seeking to use the deed of variation to “smear mud”, adding: “It’s something that my mother did 20 years ago, that was a decision she made.
“Let me just say this: I paid tax as a result of that transaction, I’ve avoided no tax in that.”
Former director of public prosecutions Keir Starmer, a Labour candidate in the May 7 general election, said Mr Miliband had given a “full explanation” of his position, and that the public was more concerned about “very complicated, sophisticated tax avoidance schemes where people are moving money around the world”.
Former Conservative treasurer Lord Fink was wrong to suggest that “everyone” avoided tax, he said.
“People will take different views on deeds of variation and all forms of tax relief is in one sense intended to reduce tax,” Mr Starmer told BBC Radio 4’s Today programme.
“I think for someone in (Lord Fink’s) position to say we all do it... I don’t think that’s right. People have a strong feeling that sophisticated tax avoidance is morally wrong. It might not be criminal but it is morally wrong.”
Labour also denied that one of Mr Miliband’s aides had described the row over tax avoidance as a “Milly Dowler moment”.