We have just crossed the English Channel so this is a good point to write about our experiences with beaurocrazy in doing this post Brexit.
Pre Brexit, UK vets could issue an EU pet passport once all relevant jabs, including rabies, were up to date. The pet passport lasted the lifetime of the dog and allowed travel across Europe. That is no longer the case. You must now obtain an animal health certificate from a UK vet, leave within 5 days and arrive in Europe within 10 days, you are allowed longer if travelling by sea. You can leave by private boat but YOU MUST BRING THE ANIMAL BACK BY AN APPROVED ROUTE; which means by plane or ferry. The returning pet must have an valid animal health certificate OR an EU pet passport with up to date jabs. The new rules are complex but the information is available on .gov.uk.
I started the process last January by getting Dotty’s jabs up to date. A couple of days before I sailed I got a health certificate from PetPass in Havant. This cost £99 for 10 minutes of checking her jab certificates and her microchip and stamping preprepared forms. Most vets were charging far more for this, PetPass is run by a couple in a conservatory at the back of their house and this is all they do so keep the costs down.
With the paperwork in hand, I arrived in Cherbourg marina and presented them when I met the frontier police at the marina to have my passport stamped. They looked confused 
they didn’t know what to do with them. I showed them the page where they are supposed to sign and stamp the form. This is necessary for onward travel in Europe. They filled it out and stamped it but did not sign it, so I asked them to do that too. They had no means of checking Dotty’s microchip so the whole thing is a farce.
This form allows me to travel with Dotty in Europe as well as return her to the UK (via an approved route) within 4 months. We will be away longer than this so I plan to get her an EU pet passport within that time. French vets no longer register dogs except for French citizens so I plan to get one in Spain.
This is just one of the many crazy consequences of Brexit which was a good idea but very badly implemented. I hope that over time the mess will be sorted, but in the mean time we must jump through paper hoops put in place for political reasons, not practical ones.
Things are as complex in USA as they are in Europe but even worse when it comes. to people. Green cards (they are not green anymore) only last 10 years before you need to replace them.I renew my first one in 2010, then replacement was reasonable easy back then if expensive.In 2020 I again applied for a new one.they send you a receipt with a renewal number wich acts like green card for one year.but this time I had not been sent the card within the year, so the recipe was not valid. My driving license ran out and without valid status they would not renew it. We had gone to St Lucia for our anniversary my UK passport was still valid so entering St Lucia was no problem but the immigration orthority in St Luncia did not accept the out of date renewal notice as valid. It took over an hour for then to get clearance from US authority to clear my return, which nearly cost me our return flight. I got notification yesterday that I go for renewal interview on 28th Sept.so think yourself lucky.