SCOTS are not ready to vote Yes in next year's referendum because they still lack information about independence, Nicola Sturgeon has claimed.

The Deputy First Minister – who is in charge of the Scottish Government's independence campaign – admitted "many" people would vote No if the poll were held immediately.

She spoke out as the SNP celebrated victory in the Aberdeenshire Donside by-election, where they held on with a reduced but comfortable majority of 2025.

Ms Sturgeon dismissed Labour claims the independence referendum had turned voters against the SNP, contributing to a sharp cut in its share of the vote from 55% at the 2011 Holyrood election to 42%.

However, she also played down a doorstep survey, conducted by the SNP during the campaign and hailed by party strategists, which showed more support for a Yes than a No vote, but with high numbers of undecided voters.

She said: "I'm not over-claiming for it. But it reflects what I feel instinctively to be the case when I'm out campaigning – that there are many people in Scotland right now who, if you were to force them to vote with a ballot paper under their nose today, they might vote No because they feel they haven't quite got the information they need to vote Yes.

"They are open to be persuaded to vote Yes and that's our challenge, but it's also our big opportunity over the next few months."

She said people were relaxed about next year's referendum and added: "Labour put out polling-day leaflets saying 'vote No to separation' and people elected an SNP MSP. Labour tried to get people to vote against the SNP as a vote 'against separation' and they failed. They absolutely failed in that."

The SNP secured victory in the by-election in the early hours of yesterday.

Mark McDonald, who stepped down as a regional MSP to fight the seat, took 9814 votes, while Labour's Willie Young was second with 7789.

The Nationalists' majority was cut by more than 5000, though on a significantly reduced turnout of 39%

The by-election followed the death of veteran SNP MSP Brian Adam, who achieved a 7175 majority over Labour at the last election.

The Liberal Democrats leapfrogged the Conservatives to take third place with Christine Jardine increasing her party's vote and share of the vote with 1940 (8.3%, plus 2.3%).

The Conservatives, in fourth, avoided the disaster of finishing below Ukip, whose candidate Otto Inglis took 1128 votes, or 4.8%, just below the 5% threshold required to save his deposit. The Greens also lost their deposit.

The swing of 9% from the SNP to Labour would unseat 28 Nationalist constituency MSPs if replicated at the next Holyrood election, Labour said.

As well as eating into the SNP's majority, Labour took victory in council by-elections in Edinburgh and Fife.

Deputy leader Anas Sarwar said: "All over Scotland, the momentum is with Scottish Labour and in Edinburgh, Fife and Aberdeen, we have been gaining support. Alex Salmond's obsession with referendum is costing him lots of votes.

"This week was an important staging post on our road back and while we know we still have some way to go, we are delighted with the progress we are making."

Willie Rennie, the Scottish LibDem leader, said his party had enjoyed "triple boost".

He said: "Our share of the vote was up by a third, our number of votes was up and we were up to third place.

"As one of only two parties who saw an increase in votes in the Donside by-election, this is a solid result for the Scottish Liberal Democrats."