Hi Jo2, You could always put a pallet floor in too to stop the weeds coming up. If you layer your compost with the usual matter and shovel some wormy soil in, should come out well. We did ours like that and came out great last year, of course we did have a brilliant dry summer, so everything rotted down really well.
When we inherited our plot the previous owner has put his manure on a membrane which had rotted and we got fantasticly healthy and robust couch grass and bindweed and thistles feeding off it. So I do think it is something to bear in mind. :) busy_lizzie