An attempt by David Cameron to outflank Labour on a new constitutional settlement for the UK ran into trouble on Sunday night when a senior Liberal Democrat cabinet minister said that the plans for devolution in England should not proceed without attempting a cross-party consensus.

As Downing Street was forced to issue an unequivocal "no ifs, no buts" declaration that the prime minister would deliver further powers to the Scottish parliament, Danny Alexander, chief secretary to the Treasury, criticised the Conservatives' handling of the aftermath of last week's referendum north of the border.

"It is deeply frustrating that briefings over the last 48 hours have distracted from the crystal-clear commitment of all parties to deliver the change Scotland voted for last week," Alexander told the Guardian. He is likely to sit on a cabinet committee overseeing devolution.

An 11th-hour vow by the three Westminster leaders last week, promising more devolution if Scotland rejected independence, has been in disarray after Cameron appeared to attach new conditions. The prime minister said on Friday that negotiations on only English MPs voting on English laws "must take place in tandem with, and at the same pace, as the settlement for Scotland".

Fears that the Tories were planning to renege on the pledge were fuelled when the Scottish-born Conservative chief whip, Michael Gove, said on Saturday that it would be "impossible" to devolve further powers to Scotland without addressing the position of Scottish MPs at Westminster.

No 10 was forced to clarify Gove's remarks, saying the prime minister was committed to the timetable agreed by the three main UK party leaders to hand greater powers over tax and welfare to the Scottish parliament. A government source said: "There was an unambiguous commitment by the party leaders to deliver more devolution to Scotland on a clear timetable. That is not conditional on anything else. No ifs, no buts – that will occur."

Government sources stressed that the two proposals – further devolution to Scotland and changing the status of Scottish MPs at Westminster – should be considered in parallel and at the same time. But the sources said that progress in one area would not depend on the other.

The prime minister will host a summit at Chequers tomorrow with leading figures on the Tory right, such as the Eurosceptic senior backbencher Bernard Jenkin, to examine ways in which to restrict votes on English-only matters to MPs south of the border.

Alexander spoke out after Alex Salmond and Alistair Darling, who led the opposing camps in the referendum, challenged the prime minister over his decision to link further devolution to Edinburgh to new restrictions on the voting rights of Scottish MPs.

Alexander said that the proposals for England should be agreed with Labour. He told the Guardian: "It has always been the case that the Scottish process must be independent of any other political discussions and must be dealt with according to the timetable we set out. For wider constitutional changes it would be preferable to have all-party consensus."

The Lib Dem call for consensus means that there is unlikely to be agreement on the English element of the package by the time of the election. The Tories are making clear that, in such circumstances, they would include plans to limit Scottish MPs' voting rights in their general election manifesto. They would also attack Labour and the Lib Dems for failing to protect the interests of English voters.

But Labour and the Lib Dems are likely to find common cause over the need for caution in addressing the status of Scottish MPs at Westminster. They say that, unlike the Scottish constitutional question that has dominated politics north of the border for four decades, there has been little debate on England-only matters.

While Cameron has been urged to include measures on English votes for English laws, Labour leader Ed Miliband is also coming under pressure from some of his northern MPs. Some Labour MPs, led by the former cabinet minister John Denham, who is holding a crisis meeting of MPs at the Labour conference today, fear that the leadership has not grasped the significance of the English question. One Labour MP in the north said: "Do I think Ed gets it? No. Do I think his Primrose Hill luvvie set get it? No, I don't."

Salmond said earlier that those who voted no in the referendum would feel they had been "misled", "gulled" and "tricked" by Downing Street. Darling insisted that there could be no link between further powers for Holyrood and limiting Scottish MPs' voting rights at Westminster. The leader of the Better Together campaign told the Andrew Marr Show: "The agreement reached by the three parties, as far as I am concerned, is non-negotiable. It was promised, it has got to be delivered. Anyone who welches on that will pay a very heavy price for years to come. It is simply non-negotiable."

The proposal to devolve further powers to Holyrood is to be overseen by Lord Smith of Kelvin, a crossbench peer who will publish draft clauses for a parliamentary bill in January to be enacted after next year's election. The plans to address the West Lothian question, the anomaly whereby Scottish MPs can vote on English-only matters but English MPs have no say on devolved matters in Scotland, will be addressed by a cabinet committee. This will be chaired by William Hague, the leader of the Commons.

The two parties are interested in the proposals by Sir William McKay, the former clerk of the House of Commons, that only English MPs should sit on the committee stage of a parliamentary bill that related just to England. Such legislation could then only be passed through a double majority voting system, achieving support of the majority of English MPs and the majority of the Commons as a whole.

Downing Street received a boost when McKay said his reforms might have to be changed in light of the outcome of the referendum. He told The World This Weekend on BBC Radio 4: "You can't lower any of our solutions, immediately and without amendment, into the present situation. They will have to be tweaked – a fairly hefty tweak, more a kick than a tweak."