Reports from folks who travel through LHR much more frequently than than 1X a month - like multiple times a week - attest to the chaos that can happen there -- especially in terminal 5. Every day? - no. But between HAL issues and BA problems with its shortage of wide body airframes, etc, There is an entire forum on Flyer Talk devoted to BA and its problems. A BIG issue is conformance. One must be cleared through security 35 minutes before the scheduled boarding time. Not in the queue but through. Absolutely no exceptions -- 2 minutes late (actually 1 minute) and you won't get on the plane no matter what.

Maybe you've been lucky.

Just checked the Heathrow website and they state that a transfer time of 60 minutes is ok if the transit is in the same terminal, so you should be fine.

My only advice is to make sure at checkin, you get your connecting flight boarding pass. If not, it will really screw you up. It happened to me as I only got excuses and had to get my passes in Heathrow which they didn’t want to provide. No one was around to help and almost missed both connecting flights which would have been devastating (no other flights until the next day). Sometimes next available flight isn’t ok.

Great advice above re ensuing you have all your boarding passes either online or collected at first check in. One less thing to worry about!

I would add that even if you do not have flex tickets it may be worth contacting the airline and asking for a free change of flight. We did this one a BA /Iberia codeshare to Lima and they switched us to an earlier incoming flight without charge. Worth a try !

If you miss your connection you'll get a free change of flight. If you make your connection you'll get home earlier. I think you have nothing to lose by keeping the flights you have.

I agree. Heathrow can be chaotic sometimes, but not all the time. It's constantly changing, so you never know what you're going to get. There's no point worrying about something that may not happen. It's the Venice > LHR, LHR>SFO flights that may be a hectic connection. But, you'll save so much time by getting your connecting boarding pass at check-in. You're lucky to have your transit in the same terminal. If you had to go to a different terminal, you'd have a problem. Just double-check that you'll get on the next flight for free if you miss it, but I think you'll be fine. Let us know how you go!

We had no problem making our outbound flight, as it was 6 hours late.

I recently booked a flight with 1 hr to transfer at LHR on BA. Before booking we called to confirm it should be ok, although I would hope they wouldn't offer a connection that's not possible. I also googled around, and as said earlier in this thread, 1 hour in the same terminal should be ok. They recommend 1.5 hrs if changing terminals.

That being said, my daughter recently took a flight with similar transfer in LHR on BA. The flight from EWR was delayed. They automatically changed her connection to a later flight. All seemed like it would be fine until they arrived at LHR. The connecting flight was cancelled! As it turned out there was some glitch affecting all of UK with the passport system (or something like that). Multitudes of flights were either delayed or cancelled. They ended up spending a night in London, and flew out the next day on a flight that also had a connection (all that was available). All the airport hotels were full, so they were given a stipend by BA to book their own hotel. They had a nice night in London.

BagLady,
Lots of helpful advice above, great examples of the value of this and other travel forums.
We once learned our Lufthansa lesson. I'd queried their rep over the phone, "Are you absolutely sure that the timing will work for our connecting flight?" They'd responded 'Yes'.
Fine.
Cue me months later at the Frankfurt airport during the ever-shrinking time slot between those very flights, racing like Usain Bolt coz we had only 18.73 seconds before that connecting flight closed its doors. Adrenaline. I came this close to wiping out a stray toddler who'd stepped out in front of my path. Adrenaline adrenaline. I tripped and went flying like some movie stunt, before immediately standing up again to resume racing. Finally made it to the check-in gate in seconds flat, breathlessly...asking staff...whew... to um...delay...closing the door.........so...so...that my non-trackstar wife could catch up OK? Allright? Whew..."

Ours had been a rookie mistake. Fingers crossed for you.
I am done. the running