The PHX-LHR route can not be operated with a dedicated airframe. The plane would be arriving PHX every 2nd/3rd day in need of having its next A/B Check completed. This requires an overnight (or similar length) stay at a maint base.
The trip will most likely be flown the generic routing used for most of the TATL long hauls ... USA Maint Base --> Europe --> USA --> Europe --> USA Maint base.
There are obviously many variations, but that routing is very common.
FWIW ...
When I say "maint" here, I'm talking about scheduled maint. Obviously, line maint is done (or more likely recorded & set-up for "deferred maint") as a plane encounters issues wile "flying the line".
Narrow body (domestic/short haul intl) are typically released from maint on 3 day runs (typically, with one of the nights being on a red-eye), the end of that run being back at a maint base for the next A/B Check.
I see that since I started writing this post (during TV commercial breaks) , freeagent has replied, essentially saying the same.