Cleaning the normal grim from a white headlining on a Cabrio

Hi all,

Mine is not that dirty (1990 Cabrio) surprisingly but it needs a clean but I'm a little nervous.
It's going grey and darker marks where the liner folds of course.

My problem is that I live in an apartment and don't have a garage or access to warm or hot water.
To do any work I have to drive a few hundred yards to a shopping center car park when its closed.

So what would best work for me?
I've done a test area using cold water, mild cleaner and a nail brush. It requires a fair bit of pressure to gain a good result. But that only works where I can apply pressure and it's a little messy!

Is there a stronger product on the market that someone can recommend please?
What are the risks?
It's one thing reading and following the instructions on the label but the results can differ a great deal as we all know.

I'd rather ask the experts than experiment  :dontknow:

Thanks!

Mike  

Looks like your going to need some kind of impregnated wipes then such as flash etc. I tried all sorts on mine swarfega as it's jelly and don't drip, use a towel to pick the muck up straight away. Use a soft nail brush to agitate.
I used Ciff cleaner bit messy. Again towel needed and for stubborn magic eraser sponges.
Perhaps some microfibre cloths and a bottle of water may help?

Others will add their favourites I am sure.