Ive been having a go with orange swarfega recently (the stuff with the grit in it). Seems to shift ground in dirt, but you need a LOT of elbow grease with a very stiff nylon bristle brush. I have used a brass bristle brush for very bad areas where the grime embeds itself in the basketweave "grooves".
Its really important to wash it all off very thoroughly though using high(ish) pressure water (jetwash maybe too much).
If its only light dirt, there are some brilliant foam "surfacant" based upholstrey cleaners that are about 4 to 5 quid a tin that just "lift" the dirt off.
This stuff is pretty good and not too expensive
http://www.amazon.co.uk/Instant-Valay-AD16G-Upholstery-Cleaner/dp/B00LUS1ETM" onclick="window.open(this.href);return false;