I'd go with UA for a few reasons.

1-My interaction with UA's ground crew at LHR has always been outstanding. They have always been willing to rebook me onto non-stops, change me to earlier flights (not standby), etc and I have also received MANY op-ups from the LHR ground crew. You have a pretty decent network out of LHR to IAD, ORD, and SFO.

2--Economy + really makes all the difference in the world if you are flying economy.

3--You're a 1K

4--LHR has plenty of *A partners that fly all across Europe and Asia.

I'm biased as I am a *A guy.

Good luck!