My wife and I were a bit concerned about what appeared to be a tight connection in London. We were booked on the Eurostar out of Paris that was scheduled to arrive at St. Pancras at 1:28PM, and then on a British Airways flight out of Heathrow at 5:05PM. I was having nightmares about missing our flight, since we had to be at Heathrow at 3:05PM - two hours before flight time.
The Eurostar arrived two minutes early, and we got a cab to Paddington, arriving just before 2PM. We then caught the 2:06 Heathrow Express, arriving at terminal 5 at 2:25.
By 3PM, we were all checked in, and having lunch at Gordon Ramsey's.
It was an expensive connection (about $75 for the two of us), but it worked out just fine.
And by the way, the food at Gordon Ramsey's is Great!
I think I only took one Underground ride from Heathrow to St. Pancras, opposite your route, but surely it goes back. And there was no traffic in the subway.
Well, I hope you saw the Beatles' lyrics on envelopes and napkins at the British library next to St. Pancras :-)