Formally, you stick to the check-in times, unless you (a) know the airport (b) HBO and (c) prepared to take the risk. That is assuming you haven't had one of the communications above inviting you to check in later than normal.

In the case of T5, knowing what I know, I would never turn up late unless I had a piece of paper, or someone in BA whose name will have clout, to give me a clear green light to go later. T3 has Positive Boarding and so you can go later but you may need to haggle your way in. Other out stations, including LGW and LCY you have more leeway. But if you are in somewhere like BLL (to take a random example) with only a very limited number of flights, HBO, had a boarding pass, you know the aircraft hasn't departed London, then I would take the risk and go in later, since I know the layout and can put the time to better use that sitting in an airport.

In other words, you either play safe, or you better know what you are doing.