Whilst BCA *could* have a policy on smoking in caves, they have NO control over access. The various access agreements are either vested in clubs, regional councils, other access controlling bodies (clue in the name) and occasionally individuals.
Ownership of caves is likewise generally vested with individuals such as farmers and other land owners. BCA does not have ownership of any caves.
BCA has NO legal duty to get involved with a smoking ban in caves but could suggest an ethical/moral stance concerning smoking in caves.
The only possible statutory smoking ban within caves could be in those caves that are designated as bat roosts where EN/Natural England could potentially claim smoking was disturbing the bats.
BCA has a lot of more important issues to direct it's attention towards with its limited resources such as time, volunteers, etc. than a unenforceable and non legal smoking ban within caves. The most likely route towards a voluntary ban would be by peer pressure.