Ed Miliband has side-stepped the issue of constitutional change, saying the issue matters - but is not the priority for most voters.
Prime Minister David Cameron says all parts of the UK should have more powers after the independence referendum in Scotland, but Mr Miliband says the process is being rushed.
His comments come after former premier Gordon Brown said he was "utterly convinced" powers for Scotland would be delivered following the No vote.
But speaking ahead of the Labour Party conference in Manchester, Mr Miliband said: "The last few months have been about keeping our country together. The next eight months will be about how we can change our country together.
"Right across Britain, people are yearning for change. Constitutional change matters.
Scots voted to remain part of the UK by 55% to 45% "But we all know something else matters even more. Our country doesn't work for everyday working people and only works for a privileged few at the top. And we've got to change it."
It followed the earlier speech by Mr Brown, whose intervention in the campaign has been credited with helping to secure a No vote, and who insisted the timetable for devolution he set out two weeks ago was on track.
A resolution on more powers will be signed by him and the three main party leaders in the House of Commons on Monday, he told a news conference in Dunfermline, Scotland.
The civil service is already working on the plans, which will be published "by the end of October," he added.
He said the timetable was a "way of bringing people together" and "this is time for Scotland to unite".
David Cameron is to sign the new powers proposals on Monday "These are men who have been promise makers and they will not be promise breakers. I will ensure that as a promise keeper that these promises that have been made will be upheld.
"We will lock in today the promises that have been made and why the timetable we set out will be delivered."
He said the laws that will form the Scotland Bill, and eventually the Scotland Act, will be ready by Burns Day (January 25).
Mr Brown also praised Scotland First Minister Alex Salmond, who dramatically quit on Friday night after the country turned out in record numbers to reject a break from the UK by 55% to 45%.
The 59-year-old was a "fierce and formidable opponent" but people owed him a "debt of gratitude" for what he had done for Scotland, he said.
The outcome of the referendum vote saw 2,001,926 opting for the No camp, with 1,617,989 voting Yes to independence.
The Yes campaign won majorities in four areas, including Dundee and Glasgow.
Six people were arrested in Glasgow city centre on Friday night as police separated rival union and independence supporters.
Hundreds of people crowded into George Square, with a chorus of Rule Britannia countered by the Scottish anthem, Flower of Scotland.
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