Hello and welcome to the forum. Your collie cross is rather young to be suffering from arthritis. Hopefully rest and medication will help.
Re Hills JC, see here
for an explanation about prescription diets. The ingredient list (from Zooplus):
Ground corn, ground rice, flaxseed, chicken and turkey meal, ground soya beans, soya bean meal, protein hydrolysate, animal fat, fish oil, dried egg product, dicalcium phosphate, salt, potassium chloride, calcium carbonate, L-carnitine, L-tryptophan, Taurine.Additives:
Vitamin A (11 304 IU/kg), vitamin D3 (478 IU/kg), vitamin E (652 mg/kg), vitamin C (76 mg/kg), beta-carotene (1.6 mg/kg).
I can't see anything in there that would be helpful to a dog with joint problems except for maybe the flaxseed but you might want to confirm this with the vet by asking him or her why they think it will help.
Wainwright's grain free wet food is a much better quality product (it scores 4.8 on the Dog Food Directory) and if your dog is settled on it I would advise you not to change. There is no joint additive in Wainwright's but that is an advantage. This is because when a dog has joint disease it needs a therapeutic dose of whatever supplement you choose. Some foods do contain glucosamine and chondroitin or perhaps green lipped mussel but the amount they get is dependent on the quantity of food you are giving to the dog.
Anecdotally I have heard that the Nutravet
product Nutraquin+ is helpful but you might also want to look at green lipped mussel and devil's claw. I understand that the latter is particularly helpful - link.
Look for the better quality supplements - some are not so good.
Possibly the best thing to do with your dog is to go for short lead walks to keep the joints working but not strained. Hydrotherapy could be very useful but discuss this with your vet first. Qualified people who offer this service would want a veterinary referral.