The Tories have an electoral mountain to climb: an extra 116 seats and the biggest swing in 60 years to achieve a majority.

Recent polls showing a narrowing of the gap, giving David Cameron’s party a single-digit lead, led bookmakers to cut the odds on a hung Parliament, ie, a Commons with no party

possessing an overall majority.

The Conservative leader’s wooing of Liberal Democrat voters this week in his New Year message seemed to underline how party strategists are covering all bases.

Given the splintering of Britain’s political affiliations, it is now much harder for the two main parties to achieve an overall majority, making a hung Parliament more likely.

Some 40 years ago, Labour or the Tories needed just 10 more seats than the other to form a majority. Nowadays, it is nearer 100.

One new threat to the Tories’ bid for power is the anti-EU UKIP, which, while it might not gain seats itself, could deprive the Conservatives of much-needed MPs.

In his festive message, Mr Cameron said he hoped for an election “free from fake political dividing lines”, noting how there was now “a lot less disagreement” between his party and Nick Clegg’s.

This was given short shrift by Danny Alexander, the Inverness MP and Mr Clegg’s Chief of Staff.

He dismissed it as “vacuous spin” that would “fool nobody”.

Yet Mr Clegg has already indicated that the LibDems in a hung Parliament would not prop up the second largest party, paving the way for the Tories to form a minority government if they had the largest number of MPs.

Wooing Liberals ahead of an election is nothing new. Indeed, it seems clear Gordon Brown’s pledge to hold a post-election referendum on replacing the traditional first-past-the-post voting system with the Alternative Vote is driven by it.

While not a proportional system, LibDems might look kindly on AV as a staging post on the constitutional road to their hoped-for destination of proportional representation.

Back in 1929, Labour formed a minority government but when it hit political turbulence it tried to keep the Liberals sweet by setting up a committee to look at electoral reform. It even offered to legislate for AV.

The last time there was a hung Parliament following an election was in February, 1974. Then, Ted Heath, the Tory leader, tried and failed to cobble together a coalition with the Liberals, the Ulster Unionists and the SNP.

Labour’s Harold Wilson formed a minority government until he won a slim majority at a second election in October 1974.

This precarious position led ultimately to the Lib-Lab pact, which discussed electoral reform. Yet as the election neared, it fell by the wayside.

Hung Parliaments with minority governments do occur between elections due to defections and by-election defeats, which is what happened in late 1996 for John Major’s battered Conservative administration. In the months before the 1997

election, Labour leader Tony Blair insured against a hung Parliament by engaging in talks on constitutional reform with Paddy Ashdown’s LibDems.

Yet by the election year of 2005, John Prescott, the deputy PM, formally declared the project “dead”.

Of course, a PR-based system, which exists at Holyrood, throws up the likelihood of coalitions or minority administrations, which is what exists in Scotland at present, with Alex Salmond’s SNP Government having no overall majority.

Perhaps it is no surprise the First Minister believes a hung Parliament at Westminster is the “likely outcome”, given recent polling.

Indeed, that is Mr Salmond’s hope, which may allow a block of 20 SNP MPs to exercise a “decisive influence” in London.

His opponents will dismiss this as wishful thinking but, given the imponderable arithmetic and the high stakes, no-one can be quite sure how the next election will pan out.

Previous minority governments

1996. Death of Tory MP Barry Porter in November means John Major finally loses majority and, until May 1997 election, heads minority Tory government.

1974. Ted Heath, unable to form coalition government with Liberals, stands down and Harold Wilson forms minority admin-istration until October election gives Labour a majority of three.

1929-1931. Ramsay MacDonald forms minority Labour government with efforts to woo Liberals failing due to internal hostility in both parties.

1924. Stanley Baldwin’s Tory administration loses confidence vote and Labour’s Ramsay MacDonald takes over, heading minority Labour government.

1910-1915. Herbert Asquith’s Liberal minority government is kept in power thanks to Irish Nationalists wanting Home Rule for Ireland and Labour supporting welfare reform.