If you wanted to design a by-election in a laboratory that was perfect for an anti-system, pro-Brexit party to win, it would surely be Peterborough. Around 61 per cent of people in the constituency voted to Leave; and the contest was forced by recall when the sitting opposition MP, after being convicted of perverting the course of justice, refused to stand down and continued to represent the seat in the Commons while wearing an electronic tag.

Governing parties almost always go backwards in by-elections unless they are absolutely miles ahead across the country, and the Conservative party is not, to put it mildly, miles ahead across the country or anything like it. The Liberal Democrats, the usual beneficiaries in situations like this, have fared poorly in Peterborough even in very good years for them, and their outspoken pro-Remain position only compounds the issue.

The only difficulty for the Brexit party is that while they are not a wholly “new” party – this is very much Ukip 2.0, with all of its influential aides people who have built up a vast store of experience from their time in Nigel Farage’s old party – one of the really important ways they are a new party is data. They know that there are a lot of people in Peterborough who might vote for them: they just don’t know where they are. Labour has had a pretty good idea they were going to need to fight this election since July 2018, when Fiona Onasanya, the previous MP, was charged, and have been working it very hard.

It’s essentially a straight fight between good organisation and a favourable political atmosphere: Labour have the former, the Brexit party the latter. Whatever the outcome, it will likely trigger further panic in the Conservative party, as whatever happens, most of their vote will have been squeezed by the Brexit party.

But, as it happens, both major parties would probably be better served by losing this one. Why?

By-elections, whether to local or national government, are a useful health check for the parties’ standing in the country and the condition of their electoral machines. But they also, inevitably, set the political narrative.

On the Labour side, we know that that party’s Brexit position, which held together both Remain and Leave voters in 2017, has been under increased strain. But the big lie of Labour’s internal debate is that, just because their current position is electorally painful, doesn’t mean that either of the alternatives are any better. Labour in general, and its leader in particular, are more unpopular with Leave voters than Remain voters, and it risks further alienating them with an avowedly anti-Brexit position. But the majority of the party’s existing coalition is pro-Remain and is well-served for alternatives, whether they be the Liberal Democrats, the Greens, the SNP or Plaid Cymru.

Labour’s best bet is probably to hold its position until the Conservative leadership election is resolved, and hope that whatever the outcome of that contest, it makes the political challenge before them easier.

But in the short term, what would be keeping me up at nights were I Labour is that the evidence of every single election and poll since Brexit was delayed is that, if you an angry Leave voter and you back the Brexit party, you get a leftish pro-Remain government that stops Brexit; and if you are an angry Remainer who backs a pro-European party, you get a leftish pro-Remain government that stops Brexit. That means that Brexit voters have a high incentive to return to the Conservative party, but Liberal Democrat and Grene voters have a low incentive to return to Labour. The problem, of course, is that if Brexit voters return to the Tories while Liberal Democrat and Green voters stick with the Liberal Democrats and Greens, then the result won't be a leftish pro-Remain government, but a Conservative one.

The ideal result for the Tories – in an election which will not change their prospects for passing a Brexit deal –is for Labour to win, with a large Brexit party vote. That allows them to hammer the message that a vote for the Brexit party, even in heavily pro-Leave territory, is actually a vote for a Labour government. If the Brexit party can actually win the seat, that’s a real nightmare for the Conservatives, as it will be argued that the party can actually replace and defeat the Conservatives, and not merely act as a spoiler.

Whereas for Labour, the reverse is true. They can only play their effective cards about domestic policy outside Brexit if it looks like voters have to choose between Labour’s domestic agenda and the pro-Remain position of the Liberal Democrats, Greens, SNP or Plaid Cymru. If the pattern is that you can “keep Labour honest” by voting for a pro-Remain party but still get the Tories out, it could get very painful for Labour in a general election.

Of course, this dynamic only holds if Labour can hold off the other pro-Remain parties and finish second. If not, then they are in even more of a bind, while for the Conservatives, a Labour victory is many degrees less catastrophic than a Brexit one.

While losing a by-election in opposition would be worrying and embarrassing in normal circumstances, they might consider it a fair exchange if it gives them a compelling message for straying Remainers come a general election.