I presume that you're referring to the tories. I wouldn't necessarily refer to them as 'the brexit' party. Yes, Cameron proposed it and they held power during the transition. However, Cameron and May were both anti-brexit. I'd go to say the rest of the tory party leaders and prospective leaders just wore the badge of being pro-brexit to steal working class brexit voters, which was edivently a successful strategy.

It's strange to consider that Corbyn was practically anti-EU for most of his political career up until brexit, when he failed to define a strong stance for or against. Or pander to the result in any capacity, unlike the tories who embraced it. Starmer was too late to the party on the big issue.

This this beyond brexit and almost totally irrelevant. Fact of the matter is that the tories have sold off energy, water, railway, and in the process of squeezing the NHS like they did water(for a decade) until the nationally funded system is practically ineffective and their argument of privitisation is palatable to enough of the voter base in order to fix the problem in the short term.

The cancer of toryism is the issue, and their "i've got mine and and I don't want you to have yours at the expense of my have gots". Their working class brexit voting base is a flash in the pan thanks to Labour inaction due to pandering to the tory voters for the past 2 decades.