I would use Autoglym interior cleaner along with a soft scrubbing brush, brilliant stuff but quite a gentle cleaner.

I have always avoided using chemicals on my 40yr old TR7 DHC's hood. Very occasional use of warm water with a drop of Fairy liquid and a firm, not soft, hand/nail scrubbing brush. Because it lives in a garage it has never been damp long enough to grow algae, nor has it been exposed to much UV light, which probably explains its longevity. However, it got treated to an experimental application of ArmorAll Leather Care this year (my other car has leather seats) which has rejuvenated its appearance. For the benefit of any chemists out there it contains - 7A-ethyldihydro-1H,3H,5H-oxazolo(3,4-C)oxazole; 7-ethylbicyclooxazolidine, benzyl salicilate.

I use Rally n Race soft top cleaner on the roof of the CLK then give it a spray with Meguiars soft top roof protector once dry. I do it twice a year and the top looks great.

I used to use Ecover washing up liquid and a soft nail brush

May have a solution. The carpet cleaner bottle from a well known make has a brush and sponge attached. It's easy to fill with soft top cleaner and should do the job...hopefully.

I have used Autoglym fabric roof cleaner and protector for years. About £20 for 2 sprayers. One is the cleaner which comes with a stiff sponge which gets most crud off. Or you can use a brush to remove stubborn stains and algae. The other sprayer is the re proofer.

Always had excellent results and one set last a couple of sessions. Generally do it once a year whether it needs it or not !

Noticeable how the water beads and runs off afterwards.