NICOLA Sturgeon will launch her bid for the leadership of the SNP at the Glasgow Royal Concert Hall this morning against a backdrop of booming party membership unprecedented in modern British politics.

While the SNP lost the referendum last week, prompting the resignation of her mentor Alex Salmond as SNP leader, Ms Sturgeon now stands to inherit a buoyant political legacy with booming party membership and a social media determined not to let go of the spirit of the Yes campaign.

The resignation of one backbencher aside, Ms Sturgeon would be at the helm of a party whose membership has more than doubled in the wake of last week's independence referendum with 26,000 new members joining the SNP since last Thursday's historic ballot, in which Scotland voted 55 per cent to 45 per cent to reject independence.

The debate over the country's future sparked massive interest in politics. Prior to the referendum the SNP had 25,642 members, but by 4pm yesterday that had increased to 52,034.

There are rules in place to prevent local constituency memberships being artificially boosted ahead of local selection battles, but no such rule exists for national membership simply because no-one ever envisaged this happening. It means that the party which elects Ms Sturgeon leader, or more interestingly elects her deputy leader, will be a whole new membership. SNP chiefs have claimed their membership now outstrips that of the Liberal Democrats across the UK, making them the third largest political party. Derek Mackay, the SNP business convener, said: "These incredible figures are absolutely inspiring."

He said the rise in membership shows that it is "the SNP the people of Scotland trust to work in the best interests of Scotland".

Mr Mackay added: "We are now the third largest party in the UK - overtaking the LibDems.

"The buoyancy of the SNP in recent days also stands in stark contrast with the other Westminster parties - with the whispering campaign against Johann Lamont starting in earnest, and the Tories confirming cuts to Scotland's budget for which they will pay a heavy price at the ballot box."

He continued: "Labour in particular have much to fear from this new wave of democratic engagement - the Labour heartlands which voted Yes will never forget Johann Lamont's alliance with the Tories in the No campaign, which is perhaps why SNP support now stands at 49 per cent according to the latest Survation poll."

A senior aide to Ms Sturgeon has mooted a change in the name of the SNP to "neuter the nationalist tag". Mhairi Hunter, a Glasgow councillor and prominent party thinker, saw the chance for a rebranding as membership doubled following the independence referendum defeat.

Writing on Twitter, she said: "We have nearly 20,000 new members now. I'm thinking maybe this may the opportunity to change our name? Neuter the nationalist tag. Dunno."

The SNP reacted angrily throughout the campaign to claims that it was made up of "narrow nationalists". Ms Hunter said party growth put this slur in the past. She said: "It's inevitable many new members aren't nationalists. This is really big and challenging really. There haven't been mass membership parties for a long time, can't be business as usual."

Ms Hunter is from a well known family of SNP supporters and campaigners. Her mother was the late Allison Hunter, leader of the opposition on Glasgow City Council, and she herself has served as a policy officer at SNP HQ.

She has been Nicola Sturgeon's constituency manager since 2007 and was the SNP deputy leader's election agent in 2011.

l John Wilson, a list MSP for Central Scotland, last night quit the party at Holyrood in a protest over its policy shift on Nato. He announced he was renouncing the party whip on the issue on the basis that he had planned to wait until after the referendum. He cited the SNP's decision to abandon its opposition to membership of Nato as a key reason.