I have to reiterate that there is a 14 day cool-off period once you receive the policy wording - so phone and they have to cancel without question. Otherwise they will no doubt be dragged in front of some watchdog (or even the Watchdog)

It is an underhand and unwelcome shift in BA's selling techniques - whoever from marketing approved this change should be looking for a new job along with their compliance colleague. Things like this should always be opt-in and not opt-out, just like marketing consent.