Mr Miliband is under pressure from some Labour MPs, including Vauxhall’s Kate Hoey, to back “English votes for English laws” and resolve the “West Lothian question”, whereby Scottish MPs can have a say on matters affecting only England.
But the move would stop 41 Labour MPs in Scotland voting on English-only issues, which could seriously reduce the likelihood of a Labour Commons majority in such votes.
When quizzed on BBC radio, shadow Chancellor Ed Balls repeatedly refused to say the current system is “unfair”.
It came just hours after Mr Miliband refused 13 times during an interview to support David Cameron’s proposals for “home rule” in England, which followed the leaders’ joint pledge to give more power over tax, welfare and spending to Scotland.
Mr Cameron is holding a devolution gathering of Conservative MPs at Chequers today in the wake of Scotland’s No vote in last week’s independence referendum.
Mr Balls accused him of “not being straight with the British people” over the cost and complexity of reform.
He warned rushing the changes risked “undermining the Union we have all just fought to save”.
The Prime Minister announced within hours of the No vote that the process for looking at the West Lothian question would proceed at the same pace as the settlement for Scotland — putting pressure on Labour to agree to the move.
The issues has dominated the start of the party’s annual conference in Manchester.
In a round of TV and radio interviews about the constitutional shake-up, Mr Balls insisted: “There is no easy solution and we are not just going to come along with something which is half-baked.
“We need, after Scotland, to make sure we have constitutional change which is fair to the regions and people of England, to my constituents as well as to Wales and to Scotland. But you don’t do that on some rushed timetable decided by politicians.”
Tory London Mayor Boris Johnson has also spoken against trying to push reform through too quickly.
He said the “basic unfairness” of allowing Scottish MPs to vote on legislation which does not apply north of the border needed addressing.
But he added: “It is bonkers to say it can be done overnight.”
Among those set to attend Mr Cameron’s devolution meeting at Chequers were John Redwood, former Attorney General Dominic Grieve, former Lords Leader Lord Strathclyde and Graham Brady, chairman of the 1922 committee of backbench Tory MPs.
The Prime Minister has also asked Commons Leader William Hague to head a committee to compile a constitutional reform blueprint.
But outgoing SNP leader Alex Salmond has accused Westminster political party leaders of reneging on their pledge to hand more power to Scotland.