The Pet Travel Scheme has been designed to allow animals such as dogs and cats to travel easily between countries and avoid quarantine but also to stop spreading rabies and other diseases.
From 1 January 2012, it is easier to travel abroad with pets. The new Brexit rules for 2021 aren’t much different. Tick treatment for pets returning to the UK are no longer required. Pets from the EU and listed non-EU countries (such as the USA and Australia) still need to be vaccinated against rabies, but they no longer need a blood test. A worming treatment has to be administered by an official veterinarian at least 24h and not more than 5 days before entering the UK.
What has changed though, is the British European Passport that is no longer valid. For leaving and entering the UK British pets will need an International Health Certificate from their veterinarian, issued and signed no more than 10 days before leaving the UK.