Just a few notes about how some dogs I know handled long-haul transport, in response to quotes from comments above --
"Most animals will not go to the bathroom in their crates, but will be busting to go once you land."
I have a big dog, about 55 lbs., who was about 8 yrs old when we came over, who traveled in the cargo hold from SF to Paris (via Air France) and arrived just fine, bouncy and happy and NOT "busting" to pee. She waited a good half hour and looked for just the right spot, as she always does. We came before the UK quarantine law was changed, so I went to France first, where my dog could live with me for the 6-month waiting period (instead of in a distant and dreaded kennel in the UK).
In Paris I met several people who were transporting their dogs from the US through France to avoid putting the dogs into British quarantine kennels. Everyone reported that their dogs did fine on the long-haul trip from the US. I have friends who take their beagle to Greece and back every summer and she just sleeps under their seat (she's a really little beagle) the whole time.
"...pets that show any signs of being sedated will not be allowed to fly." My vet was definite about sedation: Don't do it. She told us that the dogs who have severe problems and die in transit are often those who have been given sedatives, which interfere with respiration.
"I want to bring my beagle with me so badly, but as we will be renting for a while, I don't think I'll be able to."
Re bringing a dog to England and looking for a rental: we did, and we had no problem. We've moved once in London and neither place had any objections to our having a dog. One landlord said, "It's not a problem. Everybody has a dog." May you have as good luck as we did.