Labour has launched a ferocious fightback against Tory attempts to link the timetable for Scottish devolution to far-reaching constitutional reform in England, insisting that Westminster must deliver on its promises to the Scottish people.

Responding to suggestions by chief whip Michael Gove that the transfer of more powers to Scotland could not go ahead without accompanying changes south of the border, Gordon Brown said on Saturday it was inconceivable that the "promise makers" could become "promise breakers".

Brown declared that the three parties had signed a resolution committing them to a swift timetable to devolve more tax and other powers to Scotland. He told an audience in Fife: "The eyes of the world have been upon us and now I think the eyes of the world are on the leaders of the major parties of the United Kingdom. These are men who have been promise makers and they will not be promise breakers.

"I will ensure as a promise keeper that these promises that have been made will be upheld."

Amid Tory calls for Westminster to drive through changes that would bar Scottish MPs from voting on solely English matters, Gove told the Times that "it would be impossible to move forward without making sure you have change both in Scotland and England".

After the no campaign's victory was announced in the early hours of Friday, David Cameron said that, as more powers headed north to Scotland, millions of English voices also needed to be heard. The prime minister said the question of ensuring English votes for English laws should be addressed "in tandem and at the same pace" as Scottish devolution.

Writing in the Mail on Sunday he added: "New powers over tax, spending and welfare are on their way to Scotland. The timetable is brisk, but achievable: a white paper by November, and draft legislation published by January. It would have to be passed in the next parliament. But this moment must not just be about securing Scotland's future in the UK – and celebrating that fact – but settling other questions whose time has come. The challenge is to make sure our UK works for all nations.

"Millions of people in the rest of the UK have been listening to these debates, watching this campaign and rightly asking, 'What will change for us? Why can't we have the same powers and the same rights as those in Scotland?'"

On Monday, Cameron is summoning key Tory figures to Chequers to discuss how to press ahead with plans to limit the role of Scottish MPs. Those attending the constitutional summit include former cabinet minister Peter Lilley, former attorney general Dominic Grieve, former Welsh secretary John Redwood and Bernard Jenkin, chair of the public administration select committee.

Jenkin said on Saturday night that it was correct for Cameron to insist that changes to the role that Scottish MPs have in scrutinising English legislation be pegged to the same timetable as further devolution for Scotland.

"The credibility of all English parties standing at the next election is dependent on this. That is why the prime minister is right to say the two processes should be in tandem," he said.

Writing on this newspaper's website, Jenkin argues that Scottish MPs have been left with "power but no legitimacy" by devolution. Demanding an "effective English parliament", he writes: "The growl in England is now a roar … if we falter in this now, this unfairness and resentment will fester."

In an interview with the Observer, Ed Miliband casts serious doubt on the timetable for reform in England and accuses Cameron of trying to push through English constitutional reform plans that looked like they had been drawn up "on the back of a fag packet". Miliband says he is committed to devolving wide-ranging powers to Scotland to a swift timetable but that it would be wrong to rush through changes in England without consulting the English people.

But making clear that he sees Cameron's plans as motivated to damage Labour, which has 41 Scottish MPs compared to the Tories' one, he accuses the prime minister of a "desperate piece of manoeuvring".

He says: "We would be incredibly wary of back-of-the-fag-packet solutions which create two sets of MPs, two classes of MPs. Why? Because you have one prime minister of the United Kingdom [rather than one just for England]."

Miliband has proposed a constitutional convention that would not report until next autumn to consider the interlocking issues.

He said: "The idea that you should get this done in sort of, you know, six months without proper consultation, without properly going out and talking to people, when you're talking about these massive constitutional issues, I don't think is very realistic."