I think Paul Davenport's point about performers intellectual copywright and the need to make an income from one's creative endeavours are precisely the reasons for the nature of the UK law already cited in this thread. So at any event or gathering where such a recording may be made and then broadcast, the rules must apply.

So commonsense suggests that a YT the family singing "Happy Birthday" is not likely to be robbing someone of an income, though it may be embarrassing for any number of reasons and, given the wording of the Act a person thus embarrassed could mount a civil legal case and the person recording and broadcasting would have to prove that they had reasons to assume that consent had been given.

I do also appreciate the point made by Jake's Rake that a YT clip can be good publicity, but the important issue is about consent and that is an explicit part of the UK law.