I recommend going for the other Brexit achievements before attempting this one. While going for the other Brexit achievements, you can very easy end up with a no brexit result.
Star a game on Normal difficulty with Bacteria.
First step
1. Start in China.
2. Devolve any mutated traits that happen.
3. You now have to wait for a pop-up for the Brexit event, which is entitled "UK votes for Brexit in referendum". Now its important that the UK does not get infected before this event. If the UK does get infected by more then 1%, then start again.
4. Save game here. You can use this save to go for the other Brexit achievements.
Second Step
1. Now, your disease should be spreading. Wait until UK is infected.
2. Once the UK is infected, evolve Water 1 & 2, Cold Resistance 1 & 2, Rash, Sweating, Skin Lesions and Necrosis.
3. Your virus should spread quickly and the UK will end up cancelling Brexit. You have to wait for a pop-up entitled "Brexit cancelled due to XXX", Achievement will then unlocked.