Grenades can be teched, Vickers does respectable damage against garrisoned units, sappers on a building flank (no windows) are fairly effective, mortars have good range, bofors suppression ability flat out destroys most if not all buildings in one barrage, not to mention doctrinal options. The UKF lack of building clearing tools is only apparent within the early game (which is still extremely critical, I get that) but they gain access to plenty of tools within a few minutes of match start. The lack of "serious play" probably has more to do with older factions being practiced more and being more comfortable rather than British overall performance.
Grenades do not counter squads in buildings. They barely counter MG's in buildings, this also requires tommies to run up close.
the idea of "Shoot at them until they die" is a very poor building counter and allows players to stall and take the map. I also do not count commanders because no faction should need P2W commanders.
Yes the mortar pit does, and you want to nerf brace, the thing it uses and needs to not die.