The Scottish National party is poised to become one of the largest in the UK after Scotland’s pro-independence parties saw a surge in membership after last week’s referendum.

As evidence emerged of the extent of the Labour no campaign’s referendum defeat in Glasgow, the SNP announced on Monday that its membership had jumped by 70% in four days. More than 18,000 people joined the party since Thursday, lifting its overall membership to a record level of 43,644.

Peter Murrell, the party’s chief executive, tweeted that this put the SNP on course to overtake the Lib Dems’ total membership to make the SNP the UK’s third largest party, outstripping the UK Independence party’s 35,000 figure on the way.

The Lib Dems retorted that their paid membership had risen by 9% to stand at nearly 44,400, following a slump from nearly 49,000 in 2012, making them the first party to record a rise in membership while in office at Westminster.

The Scottish Green party, also part of the yes campaign, reported a parallel surge in membership, with 3,000 supporters joining since Friday. Meanwhile, Labour responded to its rivals’ successes by trying to reassure Scottish voters that their pledges of significant political and constitutional reforms were sincere.

Margaret Curran, Labour’s shadow Scottish secretary, is to tour the 10 constituencies with the highest yes vote after admitting that the party had to reach out to disillusioned Labour voters who had opted for independence at the referendum.

“We have to be honest when we look at the results and see that many of the people who think that Britain can’t work for them are Labour voters,” she said at the party’s annual conference in Manchester. “They are terrified of Tory governments, they are worried about the future of our public services and their living standards have been ground down over recent years.

“We need to understand more clearly why they are angry and what we need to do about it. We need to understand why, in areas like Glasgow, Lanarkshire and Dundee, people feel so let down by our country that they want to opt out entirely. The yes campaign did not convince people that they could provide any real economic future for the people of Scotland.

“We now need to show that the UK can create the change that all the people who voted last Thursday want – a fairer, more equal, more socially just Scotland.”

Her appeal came after the true extent of Labour’s defeat in its former stronghold of Glasgow last Thursday became clear. While the turnout there was the lowest in Scotland at 75%, Glasgow city council released polling figures for all eight Holyrood constituencies showing the no vote championed by Scottish Labour had lost in every single seat.

Derek Mackay, the SNP’s Holyrood business convenor, said: “As Labour meets in Manchester, their position in Scotland grows more and more precarious. With nearly 17,000 new members joining the SNP – and Labour’s heartlands voting yes in the referendum – the Labour leadership will be increasingly worried. Ordinary Labour voters simply won’t forget [Scottish Labour leader] Johann Lamont’s alliance with the Tories in the no campaign.”

Patrick Harvie, the Scottish Green party’s co-convenor and one of its two MSPs, said the near tripling his party’s membership was proof that the surge in political engagement by voters during the independence referendum was serious.

“We’ll be going into the next election as a much bigger party than we could have imagined, and the potential clearly still exists for a dramatic realignment of Scotland’s political landscape,” he said.

“Making that happen will mean finding ways to work together. We have always been a party that seek to work with others where common ground exists, while still offering a robust challenge where we must on the core principles of the green agenda. I’m very excited to know that we’ll be doing so as a far bigger party in future.”