We are bringing our dog over, she hasn't got a passport but has to undergo a number of blood tests that AQIS require before she's allowed to enter the country.
Not sure if she still needs those tests if she has a passport try taking a look at AQIS website or try ringing the kennels that are processing everything for us as they are based in Bristol and have been extremely helpful. Overhill Kennels, Bristol here is their email address:
k9meg@overhill.co.uk if you use these kennels they will make the transport case for your dog and take the dog up to Heathrow on your behalf. We've been quoted 1,300 approx for the flight and transportation of our jack russell plus we then have to pay for her blood tests. You could also try contacting Jets4Pets or Pet Air as they have both been extremely helpful as well.
You will need an import licence from AQIS and an export licence from the UK think its DEFRA or someone like that before any tests can be done and before you can book the flights.
We re-homed our dog but things haven't worked out with my Uncle's personal relationship so we've bitten the bullet and we are brining her over even though she's 9. She is going to love it here though as she'll have a great outdoor existence and plenty of parks to walk her in plus the beach.