Looking at it from the present (oh how hindsight in the future may change this), but it seems to me that the Tories and Labour are finished - notwithstanding a major shift in policy from either of them. The whole mess reminds me of what happened to the Liberal Party of old at the turn of the Twentieth century over Home Rule in Ireland. Both parties are split, with politicians within each either falling pro or anti EU - This appears more marked in the Conservative party than in the Labour party. The biggest problem Labour has is in its heartlands. Its core voters are split between the Remainers in Scotland and the South, and the Leavers in the Midlands and North. The latest election results saw an almost complete wipeout in Yorkshire, particularly so in Barnsley as much a strong Labour heartland as if ever there was one, where Brexit Party cleared about 23,000 votes and Labour came second with 7,600. Pretty decisive me thinks. In all across the whole of Yorkshire and Humber the Brexit Party won every area with the notable exception of York which the Liberals took. So if Labour back the remain horse, then they have lost most of their voters in the northern areas (which the Liberals will do a better job at representing being less divided), if they back leave then they've lost their remain voters everywhere else. Either way I think the party is pretty much up a creek without a paddle.
There's a quiet revolution going on that the media, mainstream politicians and champagne socialists et al. haven't quite figured out.
The new forces of British politics are the resurgent Lib-Dems versus some kind of grouping around the embryonic Brexit Party (as Farage has said, six weeks old and it has swept the rest by the wayside, pretty remarkable really). The Tories and Labour offer no solutions and are too fractured to ever resolve the issue and whichever path they choose be it, remain, leave or as Labour have tried to straddle both, from the current viewpoint they're pretty much screwed.
Have no illusions, the Brexit Party's victory was resounding. The remain dominated media are trying in vain to spin it that remain won, yeah by adding all the votes of the remain team together. I'm not sure how that is helpful, that's like saying the 2nd, 3rd and 4th runners in a race won because cumulatively they ran further than the quickest athlete.