Yes, as long as the car hire company is willing to rent you the vehicle, then the car hire excess insurer should, in the majority of cases, be fine to insure you. As long as you have your licence and the DVLA has said you are able to drive, then it is generally considered to be okay to hire and insure your rented car. You will not be covered if you drive outside the terms and conditions of your rental which would include being unfit to drive.
In addition, if you are seen as being physically fit enough to drive by your doctor then there is less of a reason that the car hire company would have to refuse you when hiring a car. Do also read your policy's terms and conditions as these will tell you the exact details of your car hire and car hire excess insurance and may answer any questions you have.
If you do have any further queries, please don't hesitate to contact our team either by phone or online chat within our office hours.