Scotland will vote to break away from the rest of the UK if the Conservatives win the next general election, a YouGov poll for The Sunday Times shows.

Support for independence currently stands at 34%, with 50% of voters opposing separatism. However, 24% of those who said they opposed independence, did not know or would not vote in a referendum, said they would be more likely to back a separate Scotland if David Cameron were prime minister. If these voters switched camps, it would lead to 50% of Scots backing independence, with only 41% voting to keep the union.

Alex Salmond, the first minister, has revealed that he plans to introduce a referendum bill in January 2010 with the final draft voted on by November. The timing was chosen because the general election is expected to be in May of that year.

The findings suggest that if, as expected, the old Etonian Conservative leader is successful at the polls, his government would face an immediate constitutional crisis.

With the Tories on course to win only two Scottish seats, according to the latest poll, it would be easy for Salmond to challenge the UK government’s legitimacy and appeal to Labour voters to back him.

He is banking on a backlash against a Conservative government in Scotland, where Margaret Thatcher was reviled. There continues to be widespread resentment at her closing of the country’s traditional industries, which inflicted high levels of unemployment, and the use of Scotland as a testing ground for the poll tax.

There has been speculation that Cameron may attempt to do a deal with Salmond, handing the Scottish parliament new tax-raising powers, but there is little chance that would be enough to buy the SNP off.

Last week Gordon Brown tried to counter the SNP and strengthen the union by bowing to pressure to devolve more financial powers to Holyrood.

The latest poll of 1,355 voters also contains bad news for the contenders in the Scottish Labour leadership election.

Asked who would make the best first minister, Iain Gray, the frontrunner for the post, secured an approval rating of only 3%, compared with 5% for Andy Kerr and 7% for Cathy Jamieson, the other challengers.

Salmond remains ahead, with 41% of voters believing he is the strongest candidate for first minister. Just 8% preferred Annabel Goldie, the leader of the Scottish Conservatives, with 5% supporting Tavish Scott, the Scottish Lib Dem leader.

Support for Brown also hangs in the balance in his Scottish backyard ahead of the Glenrothes by-election, which could seal his fate. Among voters, 46% believe he should remain prime minister irrespective of the result, while 19% say he should quit if Labour loses and another 19% say he should resign now.

The SNP remains ahead of Labour in voting intentions for Westminster although the gap has narrowed since last month’s YouGov poll. It puts the Nationalists on 34% (-2) and Labour on 32% (+3), the Tories on 17%(+1) with the Lib Dems remaining on 13%.

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