The Heathrow connection planner gets mentioned here from time to time, so I thought I'd share how their minimum connection times played out in my experience yesterday.
We flew yesterday from Vienna to Heathrow to Washington (on a single reservation), scheduled to arrive at Terminal 3 at 9:25 and depart from Terminal 5 at 11:50. The connection planner said we need 90 minutes for this connection, and we had almost an hour more than that, so we were comfortable booking this connection. I knew that we'd have to take the connector bus between terminals, go through security again, and most likely take the train to the B or C gates in Terminal 5.
But our inbound flight was delayed by almost an hour. British Airways says our official arrival time was 10:20 (I guess that's when we arrived at the gate - we landed at 10:05 and were off the plane around 10:30). So according to the connection planner, we had exactly enough time to make our connection, with no margin for error. And indeed, that's pretty much how it played out. We had a wait, but not an inordinate one, for both the connector bus and security (there were signs saying that passengers with "short connections" could skip to the front the line for the bus - I asked the staff member on duty if this applied to us and was told it did not). Other than that, we ran/speed-walked the whole way through both terminals, and we got to our departure gate at exactly 11:30, the posted closing time for the 11:50 flight. We took no time out to use the restroom, grab a snack, or refill our water bottles.
I don't think we were in much danger of missing the flight - there were a lot of delayed inbound flights yesterday morning and a lot of people rushing to make their connections, and I'm sure British Airways would much prefer to hold a flight for a few minutes than pay to rebook everyone. Still, it was an exhausting and fairly unpleasant experience. If you're booking a tight connection at Heathrow (or if you inadvertently end up with one due to circumstances beyond your control), this is what you can expect.