OP’s hearing loss might be too mild, especially if it is only in one ear, for the NHS to provide aids.
I don’t mean that OP won’t benefit from wearing a hearing aid, but some audiology departments might have to ration aids due to budgetary constraints and if so then it is conceivable that they won’t provide her with one.
(As an example, my local NHS would only give me one aid, even through I have a similar moderate hearing loss in both ears 🙄).
Do Specsavers let you try the aid for a while to see if you get on with it? I ended up getting mine from Boots, and I was allowed to try a pair for a month. At the end of that month I decided they weren’t for me (in-ear, all I could hear was myself eating, I hated them) and picked a different style to try instead, which I got on much better with. But if I had decided I didn’t like them either, then I could have returned them within the month and got a full refund.
So hopefully Specsavers offer a similar trial, and if not, maybe look around at other private providers to find someone near you that does.
(And as I always say, the quality of NHS aids varies vastly between Trusts - my local trust does not supply Bluetooth aids, and the aids they do supply are big and chunky. It depends on a Trust’s budget, but don’t necessarily assume that your local NHS aids are as good as you will get privately, without doing some research!)