One way of looking at the current political landscape is in terms of the broad division between progressive and conservative forces, which we can call "left" and "right" for shorthand. If we classify the Liberal Democrats (and their previous incarnations in the SDP and old Liberal party), along with the SNP, Plaid Cymru, Sinn Fein, SDLP and the Greens, as on the progressive wing (I know, but bear with me), then the left has enjoyed a majority of the popular vote in general elections since the mid-60s. Even before this, the right rarely got over 50% during the twentieth century, the exceptions being the Salisbury administration of 1900 and the National governments of 1931 and 1935 (which depended on Labour and Liberal defectors). This run came to an end in 2015 when the right enjoyed a majority through the combination of the Tories, UKIP and the two Northern Irish unionist parties. The decisive shift was not Labour voters attracted to the Kippers but LibDem voters who deserted to the Tories after 5 years of coalition government.
That desertion produced a Tory majority which in turn obliged David Cameron to cede a referendum on the EU to placate his Europhobic right-wing. Though Cameron's decision has been cast as a catastrophic error by some Conservatives, it may paradoxically have created the conditions for electoral dominance by the Tories for the foreseeable future, though I doubt Theresa May will be thanking him personally. The original error was the decision of Nick Clegg to enter into coalition with the Tories in 2010, both because it led indirectly to Brexit and because it revealed that many LibDem voters are actually more inclined to a conservative than a progressive position. This means that the crude left-right distinction outlined above is somewhat misleading, however it also reflects the fact that voting is often a matter of virtue-signalling, with some small-c conservatives choosing to identify as mild progressives (or even pose as radicals by voting Green) essentially for reasons of self-esteem. Likewise, communitarians who align with Labour on tax and public services may vote Conservative for reasons of "stability".
This realignment of the electorate has been strengthened by May's decision to pursue a hard Brexit. Though the LibDems and their media supporters have claimed that the party is on its way back after its victory in the Richmond by-election, it remains stuck at around 10% in the polls, which is half the figure it was consistently achieving up to 2010. This is despite its opposition to the Article 50 bill and the fact that Labour isn't competing to be the HQ of the remainer irreconcilables. Barely a fifth of the 48% constituency that voted remain seem inclined to throw in their lot with Tim Farron & co. To put it another way, half of the traditional LibDem vote appears to have been lost to the right - mainly to the Conservatives but some to UKIP - or to abstention. The inevitable decline of UKIP post-referendum may see some voters shifting back to the LibDems, but it is hard to believe this will be a significant number. Most Kippers are likely to switch to the Tories or give up voting, with the real hardcore nutters splintering into various far-right groupuscules .
What centrist (and some left) pundits appear unwilling to countenance is that the 48% does not constitute an election-winning progressive base. A significant number of remainers were Conservative voters who, like their MPs, now appear to be either reconciled to the inescapability of a hard Brexit or are hoping for a fudge to limit the damage. Either way, there is no evidence to suggest they could be won over to a wider progressive platform, just as it was always naïve in the past to imagine that Tory "wets" were somehow less than Tory. True-blue remainers aren't going to vote Labour, come what may. For this reason, the belief that a Labour party sans Corbyn could somehow stop Brexit in its tracks is for the birds. Labour might well improve in the polls with a new leader and a more supportive centrist media, but this would largely represent the return of disillusioned supporters (mostly abstainers rather than deserters to UKIP) and would probably do no more than restore the party to the 35% it achieved under Ed Miliband. That's necessary but it isn't sufficient.
The bottom line is that the shift of 10% of the electorate away from the LibDems (and mostly to the Conservatives) after 2010 is likely to be the dominant factor in shaping politics for the remainder of the decade and quite possibly beyond. Labour must hope that most UKIP supporters lapse into abstention rather than commit to the Tories, and to that end the by-election victory in Stoke may prove to be historically pivotal by accelerating UKIP's decay. This is more likely than the idea that the remaining progressive half of the LibDem vote can be won over by a shift to the centre, which would require the Liberal Democrat party to be pretty much squeezed out of existence. The LibDems may be able to tempt back those voters that deserted them after 2010 for the Tories in future by-elections and local council elections, but probably not in general elections. Equally, the remaining 10% of LibDem voters are probably pretty hardcore, so the "swayables" that Labour might poach may amount to little more than 2 or 3%. That's not insignificant, but with the 35% strategy dead and the new target for government probably around 40%, Labour will need more than ex-LibDems votes to win a majority.
Like it or not, the Labour Party has to win over soft Conservative voters, which means a combination of those 2010 vintage ex-LibDems and more traditional swing voters who can be appealed to on pragmatic grounds. This doesn't mean a return to centrism and "Worcester woman" but a pitch that paints the Tories as irresponsible gamblers and incompetents who cannot be trusted to look after the interests of the people. In other words, an appeal to self-esteem and stability. This means a conscious revival of social democratic policies that address voter concerns over insecurity (i.e. against Blairite neoliberalism as much as Tory neoliberalism), over social cohesion (which means shifting the debate from immigration to inequality), and over economic regeneration (which means investment over austerity). What it doesn't mean is the distraction of Blue Labour, with all its overtones of sectarianism, which would allow the Tories to shift the political debate towards patriotism and the evils of multiculturalism and political correctness. Labour needs to revive an inclusive British identity and a positive internationalism in contrast to the Tories' increasingly isolated English chauvinism.
Ironic though it may sound after the years of Blairite managerialism, Labour needs to define itself as a party capable of better managing the state in the interests of everybody while highlighting the Tory government's preferential treatment of vested interests as it negotiates with the EU27 (the City, global capital, the rich). This doesn't mean being cautious, because Brexit will call for radical measures and new ideas. Nor does it mean being nostalgic: the "spirit of '45" can provide some mood music, but "socialism in one country" isn't feasible any longer. It probably does mean a new leader simply because Corbyn cannot project sufficient managerial competence. Labour needs to present a "people's Brexit" in opposition to whatever hot mess the Tories produce. Such a strategy also stands a better chance of rebuilding Labour in Scotland, which is vital to achieving a governing majority. The Scots are unlikely to double-down on risk and back independence in the event of a hard Brexit, unless the May government is mad enough to push them into a corner, which could allow Labour to prosper by positioning itself between the "fundamentalisms" of the SNP and the Tories.
The obvious risk is that Theresa May might achieve sufficient compromises with the EU27 to soften Brexit, so narrowing the ground between the Tory and Labour positions. This strikes me as unlikely both because the Tory right will limit her room for manoeuvre and because the compromises will likely reflect unpopular preferences - e.g. for the City. There is also little in the Prime Minister's history to suggest she has the personal charm or cunning to sway the EU Council of Ministers. The flip-side of this is that she might so alienate the EU27 that the potential for Brexit to be moderated after 2020 by an incoming Labour government would disappear. Indeed, it might be in her interest to burn all the bridges, insisting that making a success of a Tory-designed Brexit was the only option, much as she has sought to close off alternative options since she ran for party leader. To mitigate this, Labour needs a credible alternative Brexit that can command majority support. The final irony of Brexit is that it may return us to a political duopoly and the decisive role of the swing voter.