Yes, mine are NHS, fitted and supplied at the local hospital. I have hearing loss in both ears, both about the same. You know, the age related sort! If you find the single one isn't working it would be an idea to go back although it does take quite a while to get used to them so do persevere if you can.
I met a lady on holiday who had similar hearing loss to me and had paid for her aids - and the hearing test. They looked just the same, only a little smaller. And she has to pay for batteries which only last a week, while I have a year's supply. I think hers cost between £2,000 and £3,000. The nurse had told me mine cost the NHS over £2,000 - "so be careful with them" - and I promptly loose one! I can only think people go privately because they believe NHS ones are the big pink ones that sit in the ear and don't inquire.