Conservatives must not be allowed to 'run the show' on English issues in the House of Commons simply because they hold a majority of seats in England, Deputy Prime Minister Nick Clegg has said.

Mr Clegg's Liberal Democrats are arguing for proportional representation in any system of 'English votes for English laws' introduced at Westminster, in order to avoid the Tories establishing a virtually permanent majority on matters south of the border.

The Lib Dems are proposing a grand committee to consider English or English and Welsh issues in the Commons, and Mr Clegg said Tory representation on any such body should reflect their share of the vote in the general election, which stood at just 36% in 2010.

Mr Clegg was speaking as Scottish Secretary Alistair Carmichael called on Deputy First Minister Nicola Sturgeon to rule out a rapid second independence referendum, following last month's No vote.

'English votes for English laws' shot to the top of the political agenda in the wake of the referendum, after David Cameron said that further devolution to Scotland must be matched by reform of the Westminster Parliament to end the situation where Scottish MPs can vote on issues which do not affect their constituents.

Mr Clegg has called for a constitutional convention to consider the issue.

He told BBC1's Andrew Marr Show: 'I think we need a wider constitutional convention involving the public. I think we need to radically decentralise power in England away from Whitehall.

'On the very specific but heated issue of how you vote in the House of Commons on English or English and Welsh matters only, my view and my party's view is, it's got to be fair votes for English issues not Tory votes for English issues.

'I think the Conservatives think that - (even though) they only got 38%-39% of the vote in England - somehow they can run the show. We say let's create a body of English and Welsh MPs but they've got to reflect the proportion of votes fairly won at the last election.'

At the Lib Dem conference in Glasgow, Mr Carmichael said the issue of bringing Scots together after the poll was a 'big test' for the SNP leadership and Ms Sturgeon in particular, as the likely successor to Alex Salmond.

He told activists: 'We settled the independence question in a way that was legal, fair and decisive. And we won. But now the campaign is over and now we need to move the 45% who voted Yes and the 55% who voted No.

'People of Scotland voted to remain in the United Kingdom and that democratic decision must be respected.

'So now is the time to use your imagination, and to take action that really will deliver change for Scotland ... change that will benefit all of our United Kingdom.

'We can all wave flags, join protests and march if we want to. But wouldn't it be better to set those things aside, to accept the will of the Scottish people and to put your shoulder to the wheel in our common endeavour?

'For the SNP leadership - for Nicola Sturgeon - this is of course a big test. It is disappointing that she has declined to rule out pushing for a second referendum in less than three years from now.

'There is still time for her to clarify that she will push for no such thing. And I hope that she will take that opportunity.'

Scottish Liberal Democrat leader Willie Rennie said: 'Britain will never be the same again but I can assure you that the Liberal Democrats will never support a nationalist effort to create an unstable form of devolution as a ticking time bomb deliberately designed to deliver independence.

'So there is a test for the SNP - will they be like Gollum in Lord of the Rings, torn apart by the lust for the ring of independence?

'Or will they work constructively with others to create Home Rule that is stable, as well as powerful, inside the United Kingdom? That is the real test.'

SNP MSP Stewart Maxwell said: 'The Lib Dems made a vow to deliver extensive new powers to the people of Scotland - it is time for them to honour that.

'Instead of empty words free of vision for Scotland's future, Alistair Carmichael, Willie Rennie and Danny Alexander should be focusing their efforts on ensuring their Tory chums keep their promises on powers. In the past week we have seen Tory talk of three-year delays and attempts to hold Scotland's powers to ransom over English votes for English laws.

'This is not good enough. 45% of people voted Yes to independence and the other 55% were told by the No campaign they were voting for Home Rule.'