Apparently the pub's licence doesn't cover allowing a bunch of people to sit around in an upstairs room singing songs.

Is anyone in the local authority saying that a bunch of people playing social games of darts or pool requires this pub to have Premises License entertainment permission or that such a thing would be prevented without it?

Perhaps we need some more details? Who is saying that the pub's licence does not cover a bunch of people sitting and singing songs? Is the room used for other activities?

But if this LA is setting out on such a course - it should first be reasonably sure that it would be successful in obtaining a prosecution in court. The only way it can do this is to make a case that it is for the purpose of entertaining an audience and thus Regulated Entertainment.

If it truly is just a group of people meeting in the pub to provide their own entertainment and they would still do this in the complete absence of anyone who might be described by the LA as an audience - there is case law to suggest that such a prosecution would be unsuccessful.

There is none to suggest it would suceed.