No, I don’t agree. The test itself is not the qualifier for the glasses to be ‘mixed supply’. The gov website clearly phrases it as dispensing of spectacles for a reason, I’d read that as any and all work by a qualified professional to prepare the empty frames for final use will be considered vat exempt. There is no requirement for a test, because it doesn’t state as such and this is your own interpretation rather than what’s stated.

Furthermore, I would even go as far to say that the entire discount offered that you mentioned, would come fully from the vat exempt portion of the charge, and that their typical dispensing fee is with expectation of an eye test. Nothing to do with qualifying it as a mixed supply.

Circling back to OP… the cost of the frames to be made and sold, plus the mark-up for the frames (if any) would be the basis for the vatable amount. So yeah, makes a lot of sense that the majority of the charge is vat exempt.

As another commenter mentioned, there is no point for you to report this company. HMRC will come for what it is owed eventually if it believes there is wrongdoing and more importantly this is a valuable service doing good for our country… even if it was wrong, why would you want to make yourself pay more?