Boris Johnson has defined the success of his premiership by his ability to take the UK out of the European Union by October 31 and, in doing so, placed a profound limit on his scope for manoeuvre.

In the same week that Johnson entered No.10, the Liberal Democrats elected former Coalition-Minister Jo Swinson as their new leader. Swinson’s Party pose a serious electoral problem for Johnson’s Conservatives.

The 2016 referendum resulted in a radical realignment of British politics which exacerbated internal divisions within both the Labour and Conservative parties. Labour continues to struggle with reconciling its entrenched Leave and Remain-identifying elements. The Conservative’s new leadership, meanwhile, have now finally pinned their flag to the Leave-at-all-costs mast. In doing so, they hope to nullify the threat of the Brexit Party.

That commitment to the Leave coalition was epitomised by the virtue-signalling announcement of Johnson’s new cabinet. Johnson’s overarching message was evangelical; you are either with the ‘Vote Leave’ coalition – and therefore willing to risk no-deal catastrophe for the sake of ‘getting out’ – or, you are against it.

It’s an almighty gamble that depends, principally, on a Manichean dualism between Brexiters and Remainers. As a communications strategy, it is based on the belief that people tend to vote through a prism of identity and values, over rational self-interest. It therefore relies on the hope that enough people identify as ‘Leavers’ to win Johnson’s Conservatives a Parliamentary majority.

This dualism also suits Jo Swinson and the Lib Dems. Unlike Labour, the Lib Dems are antithetical to Johnson on the central Brexit issue. Consequently, Swinson can authentically position her Party as the vehicle to unite a coalition of Remain voters.

Crucially, the polarisation between the Conservatives and Lib Dems connects to a significant subplot of the UK’s electoral narrative. Despite the attacks from Labour and the Lib Dems on each other, the seats where the Lib Dems have the greatest opportunity is in Tory-Lib marginals. Paradoxically, Swinson will benefit from criticism from Labour – because the attacks reinforce her ‘Corbynsceptic’ credentials and therefore increase her appeal to Tory-Lib swing voters.

As the result of the by-election in Brecon and Radnorshire demonstrated, the Lib Dems will benefit most if they can build on the success of the first ‘Unite to Remain’ experiment, while the Conservatives continue to be damaged by the Brexit Party.

And, as Deltapoll’s Joe Twyman has pointed out, there are currently 45 constituencies held by Tory MPs that are less safe, and have higher proportions of Remain voters than in Brecon and Radnorshire. Although it is unlikely all of these could go to the Lib Dems, it still underlines the danger for the Conservatives of alienating all Remain-supporting voters.

When he became Prime Minister, Boris Johnson lit the fuse on a time-bomb which explodes on October 31. If he has not managed to extract the UK from the European Union, his premiership surely won’t survive. But, if Johnson goes for an early election – which is probably his only route to meeting his own deadline – then we may see his gamble swing a critical number of his Party’s seats in favour of Jo Swinson’s Lib Dems.