I wouldn't voluntarily see a PA, no.
The NHS model is often said to be about funding, but imo it's not. The NHS model is about seeing the most highly-trained generalist - a GP - first. And they do the thinking and, yes, the gatekeeping. The latter has a bad reputation but it is what made the NHS exceptionally good value in the past.
Of course GPs make mistakes. All health professionals do. But far more often, they hold the uncertainty that goes with a caseload that could be absolutely anything, all day long and quite often, far into the night and at weekends. I could walk into a GP's office with a question about my fungal toenail and end up starting medication for something life threatening, because I'm seeing an incredibly highly trained professional. They hold that possibility.
The constant desire on the part of governments to fiddle with the 'best trained first' model is heartbreaking. I actually don't even think they mean to destroy the system, they just think it looks easy, a GP saying 'hmm... thats probably nothing to worry about but come back and see me quickly if it hasn't gone in a month' and NOBODY TALKS about the amount of experience, thought and training it takes to do that safely because it doesn't LOOK exciting.
PAs should, if they know how little they know, refer to specialists and for tests more often than GPs. (Evidence shows that they do, though probably not as often as they should). That's going to cost us as taxpayers more. But they can't move to Australia on six figures, and the people they see will have 'got an appointment' and may complain less to their MP, until of course they're misdiagnosed.
I'm interested to see that there is a role called Doctor's Assistant which sounds brilliant - the GP says 'right, I'm prescribing this drug and referring to that service' and the DA gets on with all the paperwork and chasing while the GP or consultant sees the next patient. That is what PAs should be doing imo.