Stewart, you may have Pirelli webbing which is a fabric sheet welded to rubber strips either side, this has a wire frame that is attached to the seat frame with hooks. They are prone to split, Heart of England do an alternative.
http://www.heartofenglandmorgans.co.uk/cgi-bin/viewPage.cgi?linkName=viewProducts&__pageIndex__productListingView=3&__view__productListingView=SELECT%20FROM%20`Standard%20product`%20WHERE%20`Standard%20product`.`section`.`__elementId__`%20=%201394