Flew from NYC to LHR a few years ago with my 50lb (very loud, barking, nutty) dog via Virgin. They were amazing to deal with; exceptionally helpful, and super kind. Didn't use a pet relocation service; just did it myself. The paperwork wasn't too difficult. It was really just a question of timing -- and oh, yeah...cost.
As I say, this was a few years ago, but I think Star's ticket was abut $1500 (extra large crate). There was also a £250 fee on this side when we landed, if memory serves me correctly.