The doctor is wrong. ALL insulin users must inform the DVLA and test BG before driving.
You will have your license restricted to a 3 year license and have certain categories of vehicle removed from your entitlement.
You must also inform your insurance company.
Failure to comply with the requirements to inform both the DVLA and the insurance company will result in you being considered to be driving without valid insurance should you have an accident. Your insurance company will expect you to comply with the DVLA regulations to test before driving - failure to do so could, again, be regarded as driving without valid insurance.
Is this a case of your doctor telling you there is no need to inform the DVLA or is it a case of doctor restricting test strips? If the latter, you do have to comply with the DVLA regulations, but the doctor doesn't have to necessarily prescribe you the means to that - although the majority will when challenged.
Smidge