I moved my horse from the US to the UK. It cost between $4000 and $5000, but this was six years ago before the price of fuel got stupid, so it could have well gone up. You can keep the price down by setting it up so your horse travels with other horses. They put them in a big shipping container-like thing that's set up like stalls and can be shared by up to three horses.
I did not have to quarantine my horse for thirty days, but my vet had to write a novel and the horse had to be vaccinated against a few things within a certain time frame and she needed to be tested for vesicular stomatitis and one or two other diseases within six weeks of transport. I didn't have to worry about keeping all this straight, though, because the shipping company was in contact with my vet and dealt with all the paperwork and when the horse got to Europe, they dealt with all the customs stuff.
The one I used was called Dutta Corp, The Dutta Corp
, and they did an excellent job. They had been recommend to me by a dressage trainer who used to import a lot of horses from Europe. I may have read somewhere they might be transporting the Olympic horses to London, so if that's the case, they must be good! Anyway, I thought they did a fantastic job. They even let me travel with my horse.