While I don't think fructosamine tests are of any value if you are home testing, if you aren't then the fructosamine test is one the tools your vet uses to monitor your pet's status, ensure the cat still needs insulin and to recommend dose decreases/increases. Since this is the vet that has prescribed the insulin before, it seems to me she is putting your cat's health at risk by refusing to prescribe until you get the testing done when you have a very sound and reasonable explanation of why you can't come in right away but have agree to come as soon as you can.
I don't know the laws in the UK and if this was a first time prescription request of a new vet, I would side with the vet. It seems to me however this is unlikely to be legal issue but rather an ethical judgement call on her part. If her ethics are such that she will endanger a pet by refusing insulin to a cat she knows is diabetic for the sake of a few days, then I'd be looking for a new vet. She deserves to be reported for endangering your cat with that attitude. I'd ask her directly why it isn't illegal for her to endanger your cat's wellbeing!
If she is not the owner/head of the veterinary clinic, you might need to contact whoever is really in charge to discuss the matter. It could be a policy they have but could wave given your circumstances and she just doesn't have the authority to override that policy.
