England
Home educated young people after the end of compulsory school age can get free eye tests and NHS dental treatment plus free NHS prescriptions through education-based exemption. The main link page is here. You can click from that link to check if you have an exemption.
The exemption page has a link to forms HC11 and HC12. At the time of writing in January 2024 the HC11 form on the exemption page is Version 22 modified in January 2024 and information about qualifying young people 16+ in full time education is to be found on page 10.
“Qualifying full-time education means you must be receiving full-time instruction at a recognised educational
establishment, or in another setting similar to a school, college or university (for example, home education).
You may need to provide evidence of your full-time qualifying education, e.g. a current Child Benefit award
notice or a letter from a qualifying establishment … If you are not entitled to education-based exemption, you may be able to claim for help with health costs under the NHS Low Income Scheme – read pages 14 and 15.“
The NHS Low Income Scheme in England has a link to form HC1.
The Association of Optometrists will advise members in England on making accurate claims (When this information was publicly available for England, it was accurate. It is now members-only and cannot easily be checked. Anecdotal evidence suggests that the Specsavers chain is the most likely not to be aware of the law.
Wales
For Wales, the equivalent of the HC11 form is called Help With Health Costs in Wales and is linked from this page. At the time of writing in January 2024 the version on the NHS website was still dated 2016; page 38 has a table with information about evidence for being in education such as “child Benefit order book”.
The NHS Low Income Scheme in Wales has a link to form HC1W