I should point out that 3 hours is the maximum time that BA recommend for checking in longhaul, 2 hours for shorthaul. The minimum is 35 minutes if you have a boarding pass from Online Checkin and no checked luggage. 2 hours in this case is a lot for me. Actual recommendations from BA are here:

https://www.britishairways.com/conte...rt/heathrow-t5

The key fact for B and C gates (and A gates) is that you must be at that gate 20 minutes before departure. Unless you hear something quite specifically otherwise, you must be there for that cut-off time. If you allow 30 minutes then you have a buffer. Nowhere in T5 is more than 15 minutes walk.