Last month, we flew on BA from our home city to LHR and connected to Milan. We had a four hour layover which ending up being good. It looked like we were staying in Terminal 5 but be aware that there are different areas of Terminal 5. I think we landed at the C area and our next flight was A. I was jetlagged; it might have been the other way around. There is a train in between. Lots of walking but not particularly bad. If you wanted to hussle and knew where you were going, it would be close but ok.
The very worst part was the security into the other section. It's been a long time since I saw such a stringent fluid check and I wasn't prepared. Everything, and I mean everything, had to go into the liter-sized baggie. Toothpaste, lotion, even the little sunscreen I keep clipped to my bag. We combed our carry-on for stuff and will not be fooled again. On a previous trip from Dublin to LHR to the USA was not nearly as bad. On that trip, we used a shuttle bus to change terminals and did make it in 75 minutes.