That request is not for BA to action. I am also not familiar with the CAA recommendation you cite. The European Commission have asked for reallocation (though in general terms and not specifically aiming their comments at LHR), but this is not for them to action either.

First, it is for the 25 EU governments, acting together with the European Parliament, to action the recommendation. They would need to revise the current EU Directive relating to Slot Allocation at Community Airports. The UK Ministry of Transport (or whatever it is called this week) would then transpose the Directive into English and Scottish law, acting under the authority granted to them by the European Communities Act 1972.

Secondly, BA would be breaking EU law if they were to start selling off slot rights for money (though they could "swap" slots with other carriers that already have slots at LHR/LGW/STN).

Thirdly, BA do not own the slots at LHR. They merely own the right to get reallocated these slots every year. That right could potentially be taken away from them by changes to the law (though this would probably trigger a lengthy legal battle).

Fourthly, and most importantly, the aviation sector is about as regulated as it gets(despite "deregulation" for domestic flights in recent decades). European governments are not going to strangle their own carriers by forcing them to give up slots at their home airports on any significant scale, no matter how much the regulators want them to do so. They are especially not going to do this when North American carriers occupy dominant positions at most major US airports, holding onto their slots under the same IATA principles that apply to slots at European airports. They are not going to do this when major carriers all have their own "home" fortress hubs spread around the world, with which BA, AF/KL, LH et al have to compete every day.

The European Commission, as I say, would like to see some enforced reallocation, but they are in no real position to force the issue.