When BA (or any full-service carrier) cancels a flight for reasons other than weather, the pax will be looked after. Whilst it may well be that the airport does not have the facilities to cope with huge numbers of pax and that they are referred to a telephone reservations line, but they will be transferred to other services, given food and accommodation where necessary (once again, it could be on a "buy now, submit a claim" basis) and not left stranded!
Lo-cos can and do leave pax in the lurch!