The rules could be changing when it comes to taking your pet abroad after Brexit. From what I gather a positive result from your pets blood test will be required. You will need to get down the vets 3 months before travelling. We took our dog to the vets last week to bring his passport up to date and we were told to call back if Brexit goes ahead and they will have the exact details of what is required then. So it looks like it will be easier to bring your pet back to the UK than take it out.