The tax is paid by the manufacturer / bottler, amd then passed on down the chain to the retailers and then to the purchaser. The refund would need to go back up the chain so that the manufacturer can claim exemption. HMRC do not give back cash, they adjust your tax burden each year to acommodate errors and rebates.
I have just had to purchase a new mobility scooter which can be obtained VAT Free. I can claim because I am diabetic, no sweat. but if I was not then I would not be able to claim against any of my other co-morbidities (heart, lungs, kidneys, etc) since they are not legitimate exemption claims. So as an elderly gent I would not get my goods cheaper. Also the application has to be valid for VAT exemption, and the goods must be specific to my condition and not also useable by the general public. so a mobility scooter that is limited to 4 mph walking pace can be exempt, but not one that can go at 6 or 8 mph since that is for (old) boy racers.
The VAT restrictions are quite specific, and so sugar tax exemption would equally require similar restrictions I suspect.