I don't think excess baggage charges work on piece in the rest of the world and particularly not on your LHR-NBO leg. More likely, it's by weight. The old IATA tariff was set at 1% or so of the OW FC class fare per kg in excess. The full OW FC fare is GBP 2,888 (can you say "ouch") ?

As for why they and other airlines can do it, because that's the trade rules nearly everyone abides by (BA makes their a bit more generous by offering 23kg instead of the standard 20kg/44lb).

Your OW status might buy you some leeway but I wouldn't want to bet on it at LHR.

If you are really going to bring your full weight allowance from the U.S., I would advise asking on the BA or BD boards if anyone knows of an excess baggage/ freight forwarder at LHR. That might be the cheapest way.