The Liberal Democrats’ victory in Richmond Park has Conservatives nervous, and rightly so. Not only did Sarah Olney take the votes of soft Conservatives who backed a Remain vote on 23 June, she also benefited from tactical voting from Labour voters.

Although Richmond Park is the fifth most pro-Remain constituency won by a Conservative at the 2015 election, the more significant number – for the Liberal Democrats at least – is 15: that’s the number of Tory-held seats they could win if they reduced the Labour vote by the same amount they managed in Richmond Park.

The Tories have two Brexit headaches, electorally speaking. The first is the direct loss of voters who backed David Cameron in 2015 and a Remain vote in 2016 to the Liberal Democrats. The second is that Brexit appears to have made Liberal Democrat candidates palatable to Labour voters who backed the party as the anti-Conservative option in seats where Labour is generally weak from 1992 to 2010, but stayed at home or voted Labour in 2015.

Although local council by-elections are not as dramatic as parliamentary ones, they offer clues as to how national elections may play out, and it’s worth noting that Richmond Park wasn’t the only place where the Liberal Democrats saw a dramatic surge in the party’s fortunes. They also made a dramatic gain in Chichester, which voted to leave.

(That’s the other factor to remember in the “Leave/Remain” divide. In Liberal-Conservative battlegrounds where the majority of voters opted to leave, the third-placed Labour and Green vote tends to be heavily pro-Remain.)

But it’s not just Conservatives with the Liberal Democrats in second who have cause to be nervous. Labour MPs outside of England's big cities have long been nervous that Ukip will do to them what the SNP did to their Scottish colleagues in 2015. That Ukip is now in second place in many seats that Labour once considered safe only adds to the sense of unease.

In a lot of seats, the closeness of Ukip is overstated. As one MP, who has the Conservatives in second place observed, “All that’s happened is you used to have five or six no-hopers, and all of that vote has gone to Ukip, so colleagues are nervous”. That’s true, to an extent. But it’s worth noting that the same thing could be said for the Liberal Democrats in Conservative seats in 1992. All they had done was to coagulate most of the “anyone but the Conservative” vote under their banner. In 1997, they took Conservative votes – and with it, picked up 28 formerly Tory seats.

Also nervous are the party’s London MPs, albeit for different reasons. They fear that Remain voters will desert them for the Liberal Democrats. (It’s worth noting that Catherine West, who sits for the most pro-Remain seat in the country, has already told constituents that she will vote against Article 50, as has David Lammy, another North London MP.)

A particular cause for alarm is that most of the party’s high command – Jeremy Corbyn, Emily Thornberry, Diane Abbott, and Keir Starmer – all sit for seats that were heavily pro-Remain. Thornberry, in particular, has the particularly dangerous combination of a seat that voted Remain in June but has flirted with the Liberal Democrats in the past, with the shadow foreign secretary finishing just 484 votes ahead of Bridget Fox, the Liberal Democrat candidate, in 2005.

Are they right to be worried? That the referendum allowed the Liberal Democrats to reconfigure the politics of Richmond Park adds credence to a YouGov poll that showed a pro-Brexit Labour party finishing third behind a pro-second referendum Liberal Democrat party, should Labour go into the next election backing Brexit and the Liberal Democrats opt to oppose it.

The difficulty for Labour is the calculation for the Liberal Democrats is easy. They are an unabashedly pro-European party, from their activists to their MPs, and the 22 per cent of voters who back a referendum re-run are a significantly larger group than the eight per cent of the vote that Nick Clegg’s Liberal Democrats got in 2015.

The calculus is more fraught for Labour. In terms of the straight Conservative battle, their best hope is to put the referendum question to bed and focus on issues which don’t divide their coalition in two, as immigration does. But for separate reasons, neither Ukip nor the Liberal Democrats will be keen to let them.

At every point, the referendum question poses difficulties for Labour. Even when neither Ukip nor the Liberal Democrats take seats from them directly, they can hurt them badly, allowing the Conservatives to come through the middle.

The big problem is that the stance that makes sense in terms of maintaining party unity is to try to run on a ticket of moving past the referendum and focussing on the party’s core issues of social justice, better public services and redistribution.

But the trouble with that approach is that it’s alarmingly similar to the one favoured by Kezia Dugdale and Scottish Labour in 2016, who tried to make the election about public services, not the constitution. They came third, behind a Conservative party that ran on an explicitly pro-Union platform. The possibility of an English sequel should not be ruled out.