I'm not sure about means testing, but personally I'd be more than happy to have a ring fenced tax increase if it went to funding the NHS properly, where it is most needed.
I wouldn't notice a few quid a month or whatever.
That, and I think people should have to pay a deposit for GP appointments. A fiver or something, which if your appointment was actually necessary and you turn up on time, is refunded. If you don't turn up or you're some selfish thick parent clogging up an appointment because your brat has a sniffle, you forfeit the deposit and get told to fuck off.
There, I've sorted the NHS crisis in 30 seconds.
That reminds me of one of the chapters of Freakonomics. A nursery had problems with parents picking up late, so they introduced a system of fines for anyone collecting late.
Problem is that it made the situation worse, as people apparently felt entitled to turn up late more often, as they were paying for it.
£5 deposits for GP appointments are only a disincentive to the very poorest, who are most likely to need healthcare. I would expect that you'll get some people not trying, because they can't afford it, and subsequently ending up even more ill, while others will feel like they now have the right to abuse the system as they're paying.
It would also not surprise me if GP surgeries had already built an assumption that some appointments would be missed, into their workloads. It's not like they're famously underworked, after all.