I made this connection with two minutes to spare. Whew.

My flight from Prague got to the gate two minutes early at 9:33 am in T3. Unfortunately, it's stairs and buses. First bus takes only those in Club Europe. Get in second bus. Significant time lost with this, as compared to having a Jetway.

I run with about 50 lbs. of carry-on bags for maybe 1/3 of a mile through one corridor after another to get to the T3 to T1 bus stop. Wait for bus. At 9:51 am the bus leaves. We get to T1, but there's some empty bus blocking the stop. My driver honks; clueless other driver moves his bus out of the way. Off the bus at 10:00 am.

Again, time to sprint. Good thing I was wearing my running shoes -- I ran the Prague Marathon yesterday; legs were not 100%. Get to security screening. Slow! Painfully slow! The lines weren't very long, but the screeners were taking their time. I was running out of time.

Get to the main hall at T1, confirm the gate for my United flight to SFO -- gate 32. Ran past the El Al lounge, left turn, long corridor. I look left through the windows to see that the United 747 is at the farthest gate. Ugh.

I show up at 32 and...it's still open. A few security questions, and I'm in. It was 10:23 am -- departure was at 10:35 am. The agent told me that I made it by two minutes. They were just about to close the gate.

So...I can't say I recommend leaving only 60 minutes connection time when you're changing terminals at Heathrow. The minimum time mentioned on LHR's site for this is 75 minutes, and even that might not work if you hit a long security line.

As the old saying goes, it's better to be lucky than smart. Thanks for those who gave me advice, above.