Will Brexit affect your insurance?
In a word, no. Although many well known insurers are wholly or mainly owned overseas – Ageas (France); Aviva (France) Allianz (Germany); AXA (France); OCASO (Spain); QBE (Australia) – their roots in the UK mostly stem from takeovers or mergers with existing UK insurers.
Getting themselves disentangled from the UK would cost them a massive amount and there are sufficient wholly UK-owned companies with the funds to pick up anything that is up for grabs.
Your policies are safe, especially if you use the services of a good insurance broker, who will be up to date with any market changes well before they have any effect.