When bringing your cat (or dog) to Spain from the UK, or from Spain back to the UK. There are a few options available; a pet transport company, an airline or bringing them yourself via train or ferry.
For all methods listed, your cat will need an up to date Pet Passport. This includes the rabies vaccine. Generally, the vaccine needs to be done at least three weeks before travel. Your cat will also need to be microchipped, which needs to be done before, or at the same time as the rabies vaccination. Here is a link about passports, but for more information you can contact your vet https://www.gov.uk/take-pet-abroad
If you choose to bring/take your pet with a transport company, make sure they are DEFRA registered and they are able to take animals. There seems to be a lot of companies over in Spain who say they take animals, but they are really removal companies. We have worked with TransPet and would definitely recommend them. They are lovely people and their van is excellent. They have individual cages in the van and the van is climate controlled at all times. The van also has a bed, so there is always someone with your pet. Here is a link to their website http://www.trans-pet.co.uk/index.html
Another option is with an airline. For routes from the UK to Spain and Spain to UK pets have to travel in the hold. This isn’t as bad as it seems as the hold is climate controlled and the pilot and crew know the animal is on board. See the blog for our experience bringing our cats via air. There is a list here of airlines certified to take animals https://www.gov.uk/government/publications/pet-travel-approved-air-sea-rail-and-charter-routes-for-the-movement-of-pets/approved-air-routes-for-pet-travel
Finally, you may opt to bring your animal yourself, either through France or via ferry from Santander/Bilbao. Brittany Ferries offer pet friendly rooms, but these are often booked up quick. There are pet friendly hotels on both routes, a quick Google search will show many options.