Bea65, I really do sympathise. I am planning to change my car this year - I am a competent and confident driver generally. I still drive around 10k miles per year, on all manner of roads. I would happily set off to drive a couple of hundred miles, and to new/different places. But I quail at the very thought of a test drive, driving a car that doesn't belong to me, with a complete stranger in the passenger seat.
It will be lovely to have a nice new(er) car though.....I am convincing myself that the gain will outweigh the pain. You can do this - just as I can. Just take as much time as you need in the car before pulling off - the sales person will not be in a rush - they are not there to test your driving skill - they want to sell you the car and will do everything they can to support you. Remember that you only need to use the basic controls for a test drive (clutch, gears, brake and accelerator). You will have plenty of time to become familiar with the whereabouts of all of the lights, wipers, heater, radio etc once the car is yours.
My mum went through this after DD died, when she was 89! The sales staff were lovely and patient, everywhere we went. She tried out about 6 different cars before she decided on the one she wanted. The staff got the car out of its parking spot into a clear space on the forecourt, and reparked it afterwards. So all she had to do was some very straightforward driving, albeit on unfamiliar (to her) roads. And she is still driving her lovely little bright red Suzuki Swift.