The Labour Party could be facing a a landslide defeat on May 3 in the elections to the Scottish Parliament and the loss of more than 500 seats in local council elections in England. In the latest Sunday Times YouGov poll, the Conservatives have an eight-point lead over Labour, by 39 per cent to 31 per cent, and a 23 per cent lead over the Liberal Democrats. That would be sufficient for the Conservatives to win more than 300 parliamentary seats at a general election. These are some of the headline results of the weekend polls. They make bad reading for Labour and for the Lib Dems.

Three big questions arise from these polls. Can the Conservatives win enough seats in Parliament at the next general election to form the next Government? Can Alex Salmond and the Scottish National Party win enough seats in the Scottish Parliament to form the next Government of Scotland? Will there be a serious challenge to Gordon Brown as the next leader of the Labour Party? If the answer to the first two questions is “yes”, the answer to the third may be “yes” as well.

Colin Rallings and Michael Thrasher, of the Local Government Elections Centre at the University of Plymouth, are the leading statisticians of local government elections. They have recently published their Media Guide to the new Parliamentary Constituencies, an invaluable reference book that will be used by the BBC, ITN and Sky News at the next general election.

It is notoriously difficult to convert percentages of votes into percentages of seats. In the past three elections, changes in tactical voting in the marginal seats threw out even the most sophisticated electoral projections. However, Rallings and Thrasher are brave men. In their Appendix 8, they provide a formula for converting shares of votes into seats. If one applies this formula to the latest YouGov poll, the Conservatives would win 302 seats, Labour would win 261 seats and there would be 55 seats for the Liberal Democrats. The next Parliament will have 650 seats, of which one will be the Speaker’s; 325 seats will therefore constitute the overall majority. On current polls neither the Conservatives nor a Lib-Lab coalition would win an overall majority, though both would be quite close.

However, the Rallings-Thrasher formula may prove to be too favourable to the Lib Dems. The YouGov poll suggests that there has been a 6.5 per cent swing from the Lib Dems to the Conservatives since 2005. Such a swing would in theory give the Conservatives 26 seats which are at present held by the Lib Dems, of which 12 would be in the South West of England. One should probably adjust the numbers of Conservative and Lib Dem seats on the Rallings and Thrasher formula to make an allowance for these potential losses.

The polls suggest that there may be a change in tactical voting. So do the reports of Conservative canvassers for the local elections. In 1997 and 2001, and to a lesser extent in 2005, Lib Dem and Labour voters were united in giving a priority to getting the Tories out.

Now Conservative canvassers, at least in southern England, are finding that most of the disillusioned Labour voters, of whom there are quite a few, are moving directly across to the Conservatives, rather than shifting to the Lib Dems. The last time that happened was in 1979. The answer to the first question (will the Conservatives be able to form the next Government) is therefore that on current polls they are getting close to power, but that they still need a few more seats if they are to win an outright majority.

The second question is Scotland. Will May 3 be the crucial day on which the Scottish voters put the SNP into power in the Scottish Parliament? That would open the way for a referendum on Scottish independence. Scottish Opinion, in the Mail on Sunday, published a poll that gives the SNP 40 per cent of the constituency vote, Labour 28, and the Conservatives and Lib Dems about 15 each. Professor John Curtice, of the University of Strathclyde, suggests that this might produce 56 seats for the SNP, 40 for Labour, 17 for the Tories and 13 for the Lib Dems. There are 129 MSPs, so 65 seats constitutes a majority.

The SNP is therefore in much the same position in Scotland as the Conservatives are in Britain. On the current polls, the SNP needs another nine seats to win a majority. At Westminster, the Conservatives need about another 20 seats, on top of current expectations. Both parties have political momentum on their side, but the Conservatives may have to wait two or three years for the next general election. Of course, they may pick up further support if the next election is too long delayed. Equally, the SNP could pick up support between now and May 3. Momentum is a powerful political advantage.

The third question is Gordon Brown. He still has preponderant support for the leadership inside the Labour Party. The YouGov poll shows that he outscores David Miliband — who is the most credible of the other possible candidates — by five to one among Labour supporters. Mr Brown has strong links with the trade unions and in Parliament, though he has many more political enemies then Mr Miliband.

Among voters as a whole, Mr Brown is also ahead of Mr Miliband, but only by 43 per cent to 31 per cent. The killer question for Mr Brown is whether he is fit to be Prime Minister. Twenty-seven per cent think he is, but 57 per cent think he is not. At the moment Mr Brown is particularly unpopular for his taxation of pensions, a broad issue that affects a large number of voters. Pensioners have a high turnout at general elections.

Until a couple of weeks ago Mr Brown’s intellectual ability, his wide network of supporters, his dominance in Parliament and his leadership in Scotland made it very unlikely he would be defeated. After May 3, the Labour Party may have to recover from two serious electoral defeats, in Scotland and in England. Who knows whether the Labour Party will then go for a younger face? The Tories did with David Cameron, just as Labour did with Tony Blair.

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