Will I still be able to use my insurance to drive in other EU member states after the UK's exit from the EU?
Yes. Your current motor insurance cover will still give you the legal minimum motor insurance needed for travel to EU & EEA countries, Serbia, Switzerland and Andorra. You won’t need to buy additional third-party motor insurance policy cover when travelling to these countries with a UK-registered vehicle.
But you should check the terms of your cover, as the minimum requirements may not be the same as the full cover you have when driving in the UK. You may wish to ‘top up’ your cover for driving abroad (e.g. comprehensive cover, which would include damage to your vehicle).