The problem with describing programmes as 'British' undermines that some of these are very obviously reflective of where the programme is set, and that is often a core element that 'makes' the programme: Derry Girls is mentioned in the article and any sane person would identify it as specifically portraying Northern Ireland, just as Still Game so obviously portrays Glasgow.
I'm not entirely sure I'm understanding the issue you have with this.
The mentioning of Carry On's isn't helpful, being the outdated institution it is, but if Derry Girls is reflective of Northern Ireland, then Eastenders is reflective of London. Does that make one or other of these programmes more or less British? I don't think it does.
I also think he has a valid point about the effect the streaming giants have on TV, whilst in some cases they do reflect a cultures identity, so "The Crown" (whether you like it or not) is British in my eyes. "Sex Education" less so, as there is a deliberate attempt to muddy the cultural id of it's setting. Naturally, a lot of the programmes on the streaming services are designed to appeal to as wide a global audience as possible. That would, I think, mean that they are unlikely to take a punt on anything like Fleabag.
It may be that you are objecting to the idea of Britishness, which is a valid viewpoint.
But In terms of safeguarding the specific unique nature of TV in our disunited kingdom I don't have a particular beef with his comments, whether this bunch of incompetents are capable or really willing to do that is another question entirely.
