I’ve traveled back and forth to europe from the uk on the ferries quite a lot with the dog. It’s all pretty straightforward with the pet passport system however you must make sure everything is correct when you turn up for your trip. Any errors or bits unsigned etc and they simply won’t let you back in the UK – it happens a lot at calais in particular, i’ve seen lots of angry/disappointed people in the pet check area.
It’s also worth noting that the longer ferries can be a bit brutal for a dog – the hull-zeebrugge for example has all the dogs in a shipping container on the car deck. They have an individual cage but it is not a good experience for them and especially not for a new dog you don’t know well. Our dog is very confident but I wouldn’t do that route again. The best ferry by far for dogs is the Harwich – Hook route, it has a special room for the dogs (still in decent cages), you can visit them when you want and take them on a deck area for a walk, fresh air and pee. Best of all you can see them on the cctv channel in your room so you don’t need to keep checking on them and potentially disturbing them.
Lastly the harwich – hook route is the only sea route out of Britain on foot with a dog and no car. Every other route requires the dog to be in a vehicle on the ferry