After reading this earlier I signed in via the link to AARP which went to the BA booking site. In the two hours I debated on whether or not to go ahead and buy it on impulse, the non-stop from SFO or PHX to LHR went up about $175 each way. There were still many options with connections, but I much prefer non-stop flights.
I decided to go PHX-LHR-PHX in late April, 2016. Thinking it might just be too good to be true, and before entering my credit card # called BA. On the phone for 47 minutes, the operator stated that, yes, it was the actual fare including taxes/fees, and it was non-refundable, however, as stated on the payment page, you can cancel for a full refund within 24 hours of booking.
While on hold with BA, I signed on to our other computer and, just for fun, typed in the same itinerary, business class: $15,700. Of course, I'd never pay full price for such a ticket, but my final payment was $1600 + $226 for choosing my seat assignment.
I look forward to the research and planning as it's been years since I visited London.