Colin,
I think most things have been covered already, but from a legal position here you go!
Driving while awaiting an initial review of your license is illegal on at least two accounts:
Driving without a driving license as your license has at this stage technically been revoked.
Driving without insurance.
As stated above your GP or Consultant cannot decide if you can drive or not, you can't as you've surrendered your driving license until DVLA determine you are fit to drive.
What changes is when your license needs renewing in 'n' months or hopefully years time, DVLA will write to you telling you that its time to fill in a mass of paperwork, DO NOT put this off, do it the day it arrives, they drag their heals and their clock starts when they get it back. My experience is that they are slow and run to the 11th hour.
During this time you are still able to drive vehicles within the classes they allowed you to drive. If you haven't received your license by the expirey date then legally you can't continue to drive past that date. Unless you have it in writing from DVLA that your license is on its way back to you. Good luck to you if you get stopped at that time!
At review times, or 3-6 months before I'd make comment to your medical practitioners that you're due a DVLA review.
Keep clear of hypos where possible, keep your levels in good shape, especially your HbA1C as this is so often how the medics review your overall control. And a dodgy reply from your Doctor or Consultant can hamper the renewal, either it being declined or the new license being shortened before the next review.
On the point of insurance, yes, you have a legal responsibility to inform your insurers and every insurer in the future. In the case of a company car, you should put this in writing to the person who is responsible for the running of the company fleet, not perhaps your manager. If in doubt, I'd send it recorded delivery to the Company Secretary at the companies registered address - this may be a different address to where you work. Your back is then covered as you have informed them. Don't forget, changing jobs in the future means you must tell your new employers, so that they can inform their insurers.
Hope its not too long before you're back behind the wheel - test regulary, especially if your sensitivity to hypos is low.
David