Step 2, getting across the Channel

Let's get the biggest problem out of the way first:  Eurostar doesn't carry dogs or pets at all, except guide dogs.  And most ferry operators won't let foot passengers take dogs either.  In fact, there are only two ferry operators who let foot passengers take dogs, DFDS Newhaven-Dieppe and Stena Line Harwich to Hoek van Holland.  You could of course dress your dog as a guide dog, pretend to be blind, and take Eurostar.  Indeed, I'm only half joking, as the Eurostar journey would be so simple compared to some of the other options, though I must admit I haven't yet heard from anyone who has actually tried it.  Difficult to be convincing if your dog is a Yorkshire Terrier, unless he's a very good actor.  But more realistically, here are the options for crossing the Channel with your dog or pet: