If a Peripatetic to the UK with a cat, it should follow the pet relocation rules. Here is some of the information for the pet owner about the vaccination and health certificate required for the cat relocation.

Microchipping for Peripatetic to the UK with a cat
Microchipping for the cat before the relocation. You must microchip your cat with an ISO-compliant 15-digit non-encrypted chip before pet relocating to the United Kingdom. Implant the microchip before giving the rabies vaccine, or the vaccination will not be valid. If your cat has a non-ISO-compliant microchip, always carry the portable scanner or have the cat re-chipped with a compliant one. Include the microchip number in the health certificate for non-EU countries and in the pet passport for EU countries.
Vaccination for the peripatetic to the UK with a cat
You must vaccinate the cat against rabies before the transport and give the vaccine after microchipping. You must ensure that the cat receives vaccination at least 21 days before traveling and that it remains up to date. The vaccine must be in active, and it must be approved by a veterinarian. If you have vaccinated the cat, you must keep the booster dose up to date. The different name of the vaccination of the cat is Kitten and Adult CRP, CRP|Anti Rabies. Other than that, the documents must include the microchip number, date of vaccination, vaccine manufacturer, and expiry date of the vaccine.
EU pet passport
If you’re traveling to an EU country, you can travel with an EU pet passport. If you are not traveling to a EU country, then you must carry the animal health certificate followed by the veterinarian. UK-issued pet passports are no longer valid for travel to the UK since Brexit; you’ll need an AHC instead.
Restriction
The UK allows all cat breeds for relocation, and it only requires a blood test if the cat comes from an unlisted third country. That means you can bring any cat breed in the UK as long as they meet the required health transportation regulation. Checking the airline’s policy, some flights have some of the breed restrictions because of only health reasons for the cat’s sake; examples of the breeds are brachycephalic and Persian cats.
Rabies titer test
You do not need the rabies blood test to bring the cat from origin country to the UK. You only need it if the cat is coming from a country not listed as rabies-controlled. If a blood test is required, you must do it thirty days after the rabies vaccination. The licensed laboratory should perform the test. The rabies antibody level must be at least 0.5 IU/ml.