How do I clean my fabric dining chairs?

[midnightmoon8]

Stupidly (I now realise!) I ordered plain cream dining chairs and they are now showing signs of grubby marks where you pick them up to move them in/out (despite the fact I always try to make sure we do so with clean hands). Any ideas on how to clean them please without staining? Thank you!

I have oak dining chairs with cream coloured fabric seats ( looks like mock suede). They get filthy. I scrub them with a sponge soaked in vanish and hot water. I rinsed the cloth out many times and keep scrubbing. Then I dry them in the sunshine and they are beautiful again.