I’m not the biggest Twitter user but I didn’t find it that difficult to get what I wanted out of it.
You already discovered the secret: You get more of what you engage with. If you don’t want to hear a lot of Brexit talk, don’t engage with Brexit content. Unfollow people who are talking a lot about Brexit
If you want to see more of something, engage with it. Click like. Follow those people. Leave a friendly comment.
On the other hand, some people are better off deleting social media if they can’t control their impulses to engage with bait. If you find yourself getting angry at the Brexit content showing up and feeling compelled to add your two cents with a comment or like, then I suppose deleting your account is the only viable option.