I've tried numerous different paths to this achievement, all of which failed miserably. Most had similar steps, but the details differed. So I took a few common threads, mixed them up a bit, and here's what ended up working for me.
Bacteria on Casual with the following genes:
Metabolic Hijack - None of the others are really necessary, so why not let the bubbles pop themselves?
Creationist - We want as few random evolutions as possible.
Native Biome - We want the disease to spread fast at the start to get more points.
Rurophile - This'll help the disease spread quickly in regions that are NOT Britain, which is important.
Sympto-Stasis - Not really important, just noting it because this is what I used...probably doesn't matter though.
I chose East Africa as my start, but anything with the opposite biome from the UK will be fine, the further away the better.
Step 1: I evolved Insect 1 and Water 1, and nothing else. After that, just let the disease spread, and devolve any symptoms that spontaneously evolve. It's okay if Britain gets infected, it shouldn't spread too quickly. Once Brexit triggers, save.
Step 2: Wait for the UK to get infected if they haven't already. Save again.
Step 3: Evolve Insomnia, Paranoia, Seizures, Insanity, Cysts, Hypersensitivity. Devolve Insomnia, Seizures, Cysts.
Step 4: Wait. You don't need anything else, and you don't want the infection rate to speed up. If the UK gets to 100%, Brutal Brexit won't pop, so you want them to be infected as slowly as possible. Eventually the Brutal Brexit bubble will pop up and the achievement is yours!
Note that Hypersensitivity may not be a requirement, but it was a common thread in multiple solutions so I used it. The achievement may be possible without it, but you'll have a ton of DNA points available so it shouldn't really matter.