David Cameron will face calls to take the unprecedented step in modern peacetime of postponing next year's UK general election by 12 months in the event of a vote for Scottish independence to avoid the prospect of a Labour government that would depend on Scottish MPs.

Amid warnings of a "constitutional meltdown" after a yes vote, which would place severe personal political pressure on the prime minister, a growing number of Tory MPs are saying they will call for legislation to be introduced to postpone the general election. It would be the first time since 1940, a year into the second world war, that a general election would have been postponed.

One member of the government said: "You would see very quickly after the referendum calls for a delay in the election. You simply could not have an election that would produce a Labour government supported by Scottish MPs if the Tories had a majority in the rest of the UK. So you would say: OK Alex Salmond wants to negotiate the break up by March 2016. So we will have a general election on the new Britain in May 2016."

There is a growing sense of panic among MPs from all parties at the prospect of a yes vote after a YouGov/Times poll showed that supporters of independence are for the first time within touching distance of winning the referendum. Support for yes has reached 47% of the vote amongst decided voters, against 53% for no with just two weeks to go.

Well placed members of the government have already started to consult the laws on postponing elections. An act of parliament would have to be passed, but there are complicating factors. The fixed term parliament act of 2011, which stipulated that the next general election would take place on 7 May 2015, would have to be repealed. The House of Lords would also be able to block the legislation because its power to delay bills by a year effectively becomes a blocking power on the eve of an election. One former law officer said: "Parliament can change elections, it can do what it likes. But it would be difficult."

Ed Miliband will arrive in Scotland for his second visit in recent weeks facing greater pressure to shore up the no vote as three former Tory Scottish secretaries published a joint appeal for the Union. Sir Edward Leigh, the veteran Tory MP, highlighted nerves on all sides when he called on the three main party leaders to "drop everything else" and campaign to save the UK.

Speaking during prime minister's questions, Leigh accused the leaders of being complacent, adding: "If we were to lose the Union, it would be not only a disaster for Scotland, but a national humiliation of catastrophic proportions."

Ruth Davidson, the Tory leader in Scotland, highlighted fears of a yes vote when she told a cross-party referendum debate on STV on Tuesday night that the Tories are on course to lose the UK election. This was seen as an attempt to reassure wavering voters who are more likely to vote for independence if they believe the Tories will win the UK election, according to the former Labour first minister Lord McConnell of Glenscorrodale.

In an email to party supporters pleading for financial support for the No campaign the Liberal Democrat, the party president Tim Farron wrote of the poll: "If that doesn't scare you, it should. We are 15 days away from an historic vote that will decide Scotland's future. If Scotland decides to go it alone the United Kingdom will be a very different place."

One former Tory minister said of a yes vote: "It would be meltdown. The major constitutional crisis would be for David. Can he hang on? I suspect he could. But it would be difficult."

Tory MPs are suggesting the constitutional crisis would be compounded by carrying on with a general election in 2015 after a yes vote. Current polls suggest Miliband will come first in the election, possibly emerging as leader of the largest party in a hung parliament. Scotland would still elect MPs to Westminster in a 2015 election because the formal break up of the UK is not due to take place, under Salmond's plans, until March 2016. Labour's tight lead in current UK-wide polls suggests Miliband would find it impossible to form either a minority government, or one in coalition with the Lib Dems, without the support of Scottish MPs. Well over 10% (41) of the 258 seats Labour won at the last election are Scottish.

David Cameron would have won a slender parliamentary majority, and would have avoided a coalition, if Scotland had been excluded from the 2010 election. He would have lost just one seat in Scotland, giving the Tories 306 seats in a 591-seat House of Commons covering England, Wales and Northern Ireland. Labour would have fallen from 258 to 217 seats while the Lib Dems would have seen their number of seats fall from 57 to 46.

Supporters of an election delay say that the most pressing task facing the UK government after a Yes vote would be to negotiate the break up of the UK with the Scottish government. Alistair Carmichael, the Lib Dem Scotland secretary, has said that Scottish MPs could not be members of the UK negotiating team. That would exclude three members of Miliband's proposed cabinet – Douglas Alexander, Jim Murphy and Margaret Curran.

The Tory MPs pressing for a delay in the election may have some political cover because Angus Robertson, the SNP leader at Westminster, called last year for a delay to allow the negotiations on separation to take place. But the House of Lords constitution select committee, which published a report on the implications of the referendum raised questions about a delay. The report said: "The extension of a parliament beyond five years would be an extraordinary step constitutionally; it may risk being seen by voters as self-serving, extending the time in power of the current government."

There would be nerves in No 10 that the PM was running scared of the electorate. One former minister said: "It is difficult to imagine postponing the election. It would not look good."

Miliband is expected to refresh his attacks on the Scottish National party's claims that it is the party of social justice. The Labour leader will address party activists in Blantyre, South Lanarkshire before leading a doorstep canvassing push; Labour officials said the party was now contacting 32,000 voters a week face to face.

During his visit to Blantyre, in a staunch Labour area being targeted heavily by the yes campaign, Miliband will accuse the SNP of hypocrisy because it wants to cut corporation tax rates, and has refused to commit itself to a higher 50p rate of income tax or a fuel price freeze.

Accompanied for the first time by the full Scottish Labour leadership team, Miliband will insist that the fastest route to a higher minimum wage, a tax on bankers bonuses and abolishing the bedroom tax was elect him as prime minister in 2015.

Citing unguarded remarks on Monday night by Ruth Davidson, the Scottish Tory leader, that the Conservatives were unlikely to win the general election, Miliband will insist that Labour would win in 2015 – a year earlier than Scotland could become independent.

"Now the SNP want to tell you we can't defeat the Tories. They are wrong. Change is coming in the UK. The Tories are on their way out; they are losing their MPs; they are defecting, divided and downhearted," he will claim.

Meanwhile, the most senior figure in the Church of Scotland, the Right Rev John Chalmers, urged campaigners to behave after a spate of clashes and incidents in recent days. Chalmers, the moderator of the General Assembly, said he had "repelled by the name-calling and rancour we have seen in recent weeks. We need to behave as though we are paving the way for working together whatever the outcome."