Battle lines are being drawn as the main UK parties figure out how to make good on their promise to give both Scotland and England more say over how they are run.
They have agreed on a timetable for giving more powers to the Scottish Parliament after Thursday's referendum.
David Cameron wants English MPs to decide England-only laws at the same time as power is devolved to Scotland.
Ed Miliband is calling instead for a debate to decide what should happen.
Scotland voted decisively to stay in the United Kingdom by 2,001,926 votes to 1,617,989 - about 55% to 45% but the pressure is now on the Westminster parties to fulfil their promise of more powers for Holyrood in the event of a No vote.
Mr Cameron has promised draft legislation by the end of January on handing more powers over tax, spending and welfare to Scotland, which would come into effect after the May 2015 general election.
At the same time, he said he had asked Commons leader William Hague to draw up plans to restrict votes on English matters to English MPs - and promised a more wide-ranging shake-up of the constitution.
Mr Cameron said: "Just as Scotland will vote separately in the Scottish Parliament on their issues, of tax, spending and welfare, so too England, as well as Wales and Northern Ireland should be able to vote on these issues and all this must take place in tandem with, and at the same pace as the settlement for Scotland."
SNP leader Alex Salmond, who announced he was standing down after losing Thursday's referendum, has warned that the timetable is already slipping because, he claimed, Mr Cameron could not guarantee that his backbenchers would vote for it.
Analysis by BBC Parliamentary correspondent Mark D'Arcy
Post referendum, almost everyone in Westminster is calling for English devolution. The trouble is that there is no agreed vision of what that actually means - which is going to make politics through and after the next general election a messy business.
Devolution to England as a whole (either via English-only votes in Westminster, or via a new, separate institution, with a steel and smoked-glass HQ in York, or somewhere) would probably mean Conservative majority rule in England, more often than not.
Devolution to regions or city-regions would mean more Labour enclaves.
So guess who favours which options?
Former Conservative Cabinet Minster Owen Paterson said: "Extensive promises have been made to the Scottish people, which will assume that Scottish politicians will continue to adjudicate on taxes raised on English taxpayers and also assume that English taxpayers will continue to shore up the whole settlement with extensive transfers of funds."
Mr Miliband has said he remains committed to the timetable for new powers for Scotland - but he will not be signing up to Mr Cameron's plan for English MP votes.
Instead, the Labour leader announced plans for a national debate on all aspects of Britain's constitution - including House of Lords reform, decentralisation of power to local government and a written constitution - as well as more powers for England, Wales and Northern Ireland.
If Labour wins the general election, this would be followed by a Constitutional Convention, in the autumn of 2015, and then by legislation.
Arriving at his party's annual conference in Manchester, which gets under way at the weekend, Mr Miliband said he would not allow the debate "to be used for narrow party political advantage".
Mr Miliband faces the prospect of his party's Scottish MPs being stripped of the power to vote on crucial issues such as health, education and finance under Mr Cameron's proposals, potentially undermining a future Labour government.
The Labour leader promised to deliver on the promise of further powers for Scotland but said "other people in Britain, including England, now deserve the chance to shape their own futures with a dynamic devolution settlement.
He added: "This must not be led just by a Westminster elite but be open to every citizen so that they can have their say."
Labour MP Graham Allen, chairman of the Political and Constitutional Reform committee, questioned whether Mr Miliband's plan would mean "nothing concrete will be in the [Labour] manifesto while the consultation goes on".
He asked, on his Twitter feed, if Mr Miliband was "boldly seizing the moment or booting English devolution into the long grass".
Mr Allen is to haul the leaders of the three main parties before his committee when Parliament returns as part of an investigation into devolution.
The party leaders are also facing demands from England's biggest cities, and its county councils, for more power to be devolved to them.
Lib Dem leader Nick Clegg - who backs David Cameron's timetable for further Scottish devolution and plans for England-only votes at Westminster - has backed calls for decentralisation of tax and spending powers to beefed-up "city regions".
UKIP leader Nigel Farage has, meanwhile, written to all Scottish MPs asking them not to vote on English issues.
"The English need to be able to debate on their issues, alone, in the House of Commons, and if Scottish MPs agree to do that it will be a very significant step forward," he said.