I expect the NHS will play down your need to see a doctor, and that it's not particularly easy to avoid being fobbed off with nothing. NTs may be more comfortable about exaggerating the severity of their ailments and in competing against the system generally. But I don't think you'd have much to lose by having a go. Might be worth researching your ailment and trying to figure out whether you really do need to be seen, and if so how you might best pitch what you say to them.
https://www.nhs.uk/nhs-services/urgent- ... ine-works/
I see they do the triage thing by asking questions, but they don't say what the questions will be. A lot of them probably depend on your symptoms. They accept people doing it on behalf of the actual patient, so if you know a more able and willing ally, you could ask them. And you don't have to identify yourself, so if you get fobbed off the first time then you could try again, preferably from another phone. And some surgeries do the walk-in thing. I gather some people are experiencing so much resistance from GP surgeries to being seen quickly that they resort to going to Accident & Emergency.
Personally I don't feel I can necessarily depend on doctors, so I tend to research my ailments for myself first, if it's anything like simple, though I'd be wary of using that as my sole source of information if it was anything that looked very serious. Ideally I'd do both every time, and hope the two sources agreed. But then ideally I'd have a lot of money and I'd see 2 or 3 private doctors if necessary.