Are you still looking for information or options on shipping your horse? I'm in the midst of shipping my Arabian (he is scheduled to arrive on a flight to Amsterdam on Sunday, and projected to arrive in London on the horse van from there on Jan 29th

). I got quotes from several shippers before picking the one I am now using.
I don't think many horses are shipped from the USA via ship anymore - as far as I understand flying is actually easier on them - I think in part because it is over and done with much quicker than them having to stand around on a boat for a week.
I'm using the Tim Dutta corporation for shipping
http://www.timdutta.com/ [nofollow] I see they've just revamped their website and it now has a nice explanation of the process of flying horses on it.
Dutta use New York to ship out of which might not be as good for you since you are in Nevada
Before settling on Dutta (who came recommended via being the US partner of a German shipping company a friend uses) I had also gotten some recommendations from people here who are involved in the Quarter Horse show scene here of a company in Oklahoma, Nedpoint Quarter Horses, who do export as well:
http://www.nedpointquarterhorses.com/ [nofollow] They actually quoted me the lowest price on the part of the process they handle, but that route would have made it so I had to ship my horse cosiderably farther overland in the USA, which would have been harder on him - so I went with a slighty pricier option that was a better route for him based on where he was starting from
AFAIK The horse passport is something you will get for your horse after your horse is in England, as the USA does not have a requirement for horses to have identification that includes their vet records with them at all times in the same way the EU countries do. (This is what a horse passport is - it's not actually a document specifically for use in crossing borders, despite the name!) The DEFRA requirement is that horse in the country for more than a relatively short time be passported, but you are definitely allowed to acquire the passport *after* the horse arrives if it is coming from a country like the USA that does not have passports as a usual thing.