You can just mix 4 parts flour, 1 part salt & 1.5 water to the right consistency, and then bake the finished product to make it "permanent." But it's not nearly as nice and smooth as the cooked kind witih oil.
But here's a no-cook recipe for "silly putty"
2 parts white glue
1 part liquid starch
I haven't used this so I don't know what happens when it dries in the carpet :(
Thanks everyone. I will have a go at the weekend. The baked one I believe is salt dough which I have made a painted but it is playdough which I will have a go at for 3yr old children. Fingers crossed it works.