I have to agree with Rainboe. BA along with most major airlines, sell a selection of special fares, only available through specialist Business Travel Agents that deal with the voluntary sector. These Charity Fares normally offer an increased baggage allowance. Some airlines will consider "any reasonable amount" of excess baggage in connection with the fare - but it has to be requested in advance. No-one should expect to turn up at the check-in counter and say "This is for Charity mate!" and have any amount of excess baggage just waived through.
BTW - maybe the most generous for this was SN, will be interesting to see if it continues in the guise of the SN Brussels/Virgin Express merger.