For peace of mind, I'd suggest that you pay for a test at an independent optician. I don't think, justified though your concerns may be (I'm profoundly allergic to hard selling techniques), that the NHS should pay for another test, but peace of mind or confirmation that those issues are there is worth the payment; you don't want to ignore it and find out later that they were absolutely right.

There have been changes to the NICE guidelines in the last year which mean that things that wouldn't previously have been highlighted during an eye test now must be mentioned and things that were previously just to be recorded in notes should be referred to hospital
eye service. Frankly some of it is a nonsense but it is what it is.

Everyone should be wearing decent UV protection for the eye, I'd say you wouldn't go out without sunscreen on but in the UK most people do and then we wonder why we're worse than Australia for skin cancers. We have shocking rates of macula disease in the UK as well and our blase attitude to wearing decent sunglasses is a huge factor (that and the cigarettes but smokers insist it doesn't do them harm as the nurse practitioner hovers over with eylea number 14 at the ready, that's another story).

The NHS won't fund another eye test, why would they? You chose your optometrist and they'll be paid in due course having carried out the work to the contract. You can choose to pay for another but you'll probably find it's a repeat of the same rigmarole and it's all to do with the NICE guidelines and possibly a clash of personalities and possibly a corporate policy to ensure those guidelines are adhered to in any mystery visits by mystery visiting health professionals spot checking their premesis.

You could always write to the manager to feed back your concerns, it won't get you another free eye test though.

Hmm if no referral was recommended then I suspect their was nothing concerning to worry about.

I would contact the practice concerneded - they may retest you with another optometrist to set your mind at rest

Although I belive the guidance does allow for a retest on the NHS I personally would not do it unless you had allowed the original practice a chance to sort out the problem.

Nearly all 2nd opinions I do end up being about communication issues / personality clashes I rarely find a signficantly diffrent presciption or diffrent clincal outcome

OP if you want a second opinion, you could look for one of the "free eye test" offers sometimes offered by well known brands. They don't exist as a constant thing so it may be a case of waiting but you'd get the test for free (just make sure to read the terms and conditions don't offer a free eye test...when you purchase glasses/contacts etc).
If you did want to pay for the test, it's normally around £10-£15 depending on where you do and they should provide you with a report on things following which you can compare with your current prescription, but bare in mind, owing to the difficulty and very precise nature of an eye test, it could be that your results vary slightly. It's no reason to feel concerned at minor differences, but chances are the test was fine because if you had gone further to buy the lenses that were suggested to you and they'd gotten the prescription badly wrong, it would do them no favors at all.