We have been having a very dry, windy winter in L.A., so the static cling thing has been a topic of discussion out here. I wouldn't use the dryer sheets, because the chemicals are bad for the cats, but there is a product called HyLyt out here which is like a spray on topical oil, but it is not tacky to the touch. I get it at the vet and when the kits get staticy, I spray some on my hand and rub it into their coats. Works fine. You could also look for a leave-in feline conditioner. Or maybe you could try the kitty bath wipes, which most pet stores carry, which is a way to "bathe" them with no water. You just wipe 'em down with it, but it helps with the static cling as well. I don't know what the product names are on the UK side, but I hope this helps.
Esther