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I think you've significantly misread the Labour vote, Oliver.
Nope. The main voters who were prepared to switch parties because of 'Brexit' were 'Leave' supporters, not 'Remain' supporters. Politics is a broad business, and there are lots of other things to care about than 'Brexit'. (Edit: As @n3il said. Not even Neils can agree. :) )
As you say, David Davis may well have been a significant factor in this changing.
I think you've significantly misread the Labour vote, Oliver.
Contrast the data in this: https://lordashcroftpolls.com/2016/06/how-the-united-kingdom-voted-and-why/
With this: https://yougov.co.uk/news/2017/06/13/how-britain-voted-2017-general-election/
And see if you can spot the potential problem.