Hey fgdevil (666) welcome to the group.
Your doctor has no right not to sign the form. All you are asking is some basic health questions, details of medication and to have your BP checked (pretty much). At my surgery they charged me £15 for the privilege of me answering all the questions for the nurse who checked my BP and got the form endorsed by the receptionist. It took all of 3 minutes. My neighbour goes to the same surgery and was not charged.
They are not giving you permission or anything, VLCD's are fully accepted by the nedical profession, and the doctor is probably justignorant and worried that they might be signing something that could implicate them in our new litigious society.
Be firm and see what happens. You could try to call the nursing practitioner and ask her if she can fill out a health questionnaire for you and check your BP. Also try to call your local Primary Care Trust and explain your problem they might be able to help.
As others have said - cut back on the carbs. I like the idea of having your favourite foods in the last couple of weeks or using all the 'bad stuff' (whatever that is) that you have in the cupboard. You can actually combine this. If you fancy Indian have a shashlick, or a tandoori dish with salad, vegetables (no sugar) and yoghurt - just avoid the naan and rice. Avoid the processed carbs - pasta, bread, rice, Avoid sugar and starches-rich veggies such as potato and fill up on protein and leafy green veggies. - You can look at some of the low carb websites for recipes and ideas.
Good luck with the doctor!