I doubt Brexit would've been much different. The constituency nature of UK general elections means that a substantial majority of MPs knew they had to support it even though it was only a 48-52 split in a supposedly advisory referendum.

But to the extent that it might have been different, the many incompatible visions for it that gridlocked UK politics might have coalesced into a single vision, and while that would still have been worse than not having done Brexit as all, it might have been less bad than five mutually incompatible visions that got brushed under the carpet long enough to make it happen only by Boris Johnson promising all things to all people.

OTOH, things can be much much worse than Brexit. Musk's tweets about civil war in the UK, his willingness to support people too far right to even be in the most far-right of the top 8 polling parties, what Grok calls itself…

On that kind of theme, there's a psych study, Robbers Cave, worth reading about. Also note some summaries fail to mention that both groups resented being manipulated by the researchers: https://en.wikipedia.org/wiki/Realistic_conflict_theory#Robb...