Under the law at present the licensee is liable, unless he or she has a Public Entertainment Licence covering this, and so are "the organisers" - but the singers aren't. Under the "reform" the singers would be committing an offence as well, and be liable to the same penalties.
Most places do not have licences to cover this kind of thing, and probably won't in the future. (Remember it's not just pubs.) So long as the local authorities turn a blind eye nothing untoward happens. All it takes is a bloody minded jobsworth or councillor, and there are a fair number of them about.
Just because something is traditional is no protection. Out in Dorset this week a local council official week moved in and stopped mummers from performing in two pubs in Cerne Abbas. I bet the people involved would have dismissed any suggestion that anything like that could happen as paranoid rubbish. Until it happened.