the doctor is saying that so that if you put your back out when cycling he doesn't get sued for telling you not to. He doesn't actually know that cycling would aggrevate the symptoms. Ask him to explain HOW cycling would aggrevate the symptoms, I bet he can't.
When I went to the doctor for a problem with my knee, i described the symptoms, first thing she said was "you'd probably best stop cycling for a week or two". I said, "no chance. If you can't find me a proper solution i'll bid you good day." The hospital deduced that I had what is called an 'expected abnormaility', which is, iirc, a deliberate oxymoron, and that I could have surgery to 'fix' it but they wouldn't recommend it as it might make it worse due to the amount of scar tissue that may form.
They did however put my mind at rest that a physio's diagnosis of a "loose fib" was wrong.
The problem was eventually fixed by me seeing a cycling coach who checked and tweaked my bike fit and gave me a bit of advice on positioning.
I would second recommendations to try a recumbent though, I really would. How far are you from cambridgeshire? there's a place there called DTek who do try out days, the bloke that runs it is quite a sound guy and for £20 you can spend several hours test riding all different sorts of recumbents in a small village with hardly any traffic.