During the 1951 general election campaign, Winston Churchill travelled to West Yorkshire to deliver a speech on behalf of a local candidate, Violet Bonham Carter. The two were old friends but it was still unusual: Churchill was leader of the Conservative party but Bonham Carter was fighting Colne Valley for the Liberals.

Churchill, however, was not simply putting friendship first. He was honouring a pact between the two parties. The Liberals, then in a parlous state, stood down in many seats that mattered to the Tories; in return, the Conservatives stood aside in seven to favour the Liberals. In the event, Labour narrowly held Colne Valley. But in other seats, the pact worked. The Liberal party just about survived. And given that the Tories emerged from the election with a majority of just 17, the pact possibly tipped the outcome in Churchill’s favour.

Today talk of electoral pacts has revived. In the Brecon and Radnorshire byelection, the Greens and Plaid Cymru are standing down in favour of the Liberal Democrats. More importantly, the possibility has been widely aired of a pact between the Conservatives and the Brexit party in the event of an autumn election. YouGov finds that a large majority of local Tory members like the idea. ComRes finds the same among Conservative councillors.

The logic is obvious. Conservatives defected to the Brexit party in vast numbers in Theresa May’s European parliament elections. Nigel Farage’s party will almost certainly be far less popular in an autumn election, when voters are choosing a government; but it could still do well enough to deprive Conservative MPs of victory in seats where Labour or the Liberal Democrats are snapping at their heels. If the pro-Brexit vote could unite behind one local candidate, rather than split between two, the effect could well be to propel Boris Johnson to a clear-cut victory rather than condemn him to defeat.

However, while the value of a pact to the Conservative party is obvious, its attraction to the Brexit party is far from clear.

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Let’s start with the assumption that Farage, like Johnson, would want a pact to maximise his party’s representation in parliament. He would therefore need the Conservatives to stand down in seats the Brexit party could win. Where are these? The most obvious are the seats with the highest Brexit vote in 2016. There were 50 where 67% or more voted to leave the EU. Where might the Tories stand down?

We can rule out the 24 seats that currently have Conservative MPs. These include Boston and Skegness, which had the highest pro-Brexit vote of 75%. That leaves 26 Labour-held, strongly pro-Brexit seats. Of these, 13 are Labour-Conservative marginals that would fall to the Tories on a 7% swing. I doubt that the Conservatives would surrender these: they are precisely the kind of seat the Tories would need to target in order to secure a clear majority in the new parliament.

We are left with 13 strongly pro-Brexit Labour seats where the Tories have no realistic chance of winning. It would cost them little to offer them to Farage. Despite doing well in all of them this May, the Brexit party would struggle to win them in a general election. They include Doncaster North, where Ed Miliband has a majority of 14,024, and Normanton, Pontefract and Castleford, where the Tories lagged 14,499 behind Yvette Cooper. In those, and the other 11 seats on this list, the Conservatives have not done well in living memory: towns and cities such as Rotherham, Hull, Barnsley, Hemsworth, Redcar and Wentworth.

If I were Farage and eying my prospects in these seats – and, indeed, the dramatic possibility of ousting Cooper or Miliband – the last thing I would want would be the endorsement of the Conservatives. Voters in these constituencies may not love Labour as much as they once did, but there is no sign that their historic antipathy to the Tories has evaporated. Indeed, Ukip did well in many of these seats in 2015 because thousands of voters found a non-Tory way of registering their dislike of the EU.

Were the Tories to stand down and endorse the Brexit party, Farage’s candidates would lose their most appealing quality in these Labour heartlands: that they offer Tory-hating, pro-Brexit voters an option that does not help Johnson. If local voters were forced to choose between their pro-EU Labour MP and a Conservative backed pro-Brexit candidate, my money would be on Miliband, Cooper and the others holding their seats.

I cannot see a Tory-Brexit party pact delivering Farage any MPs. And the downside is considerable. Not only might a pact actually reduce his party’s chances in Labour’s heartlands; by standing down in a number of marginals, the party would be diminishing its overall vote tally – a figure that does not formally matter but which has symbolic significance to an insurgent party with long-term ambitions. A pact, then, looks extremely unattractive to the Brexit party in terms of seats and overall votes. Is there anything else that might attract Farage?

The most obvious benefit is that, even if his party had no MPs, he could ensure a clear Tory majority, and hence the UK leaving the EU, by standing aside in the key marginals. Without a pact, the pro-Brexit vote in dozens of key seats would be split. Labour and the Liberal Democrats may well make the gains that would ensure a majority in the new parliament for a fresh Brexit referendum, and the UK remaining in the EU after all.

So here is the paradox. A pact could advance the Brexit party’s main cause, but destroy the party itself: with no MPs, and watching Brexit happen from the sidelines, it would lose its purpose and its future. On the other hand, the refusal to enter into a pact may well kill Brexit, but it could also wound the Tories, possibly fatally, and lead to a political realignment in which Farage may well have a big impact and a shining future. Which future would he really prefer? We may not have long to find out.

• Peter Kellner is a former president of YouGov