It's clearly some kind of chintz but it's not possible to see clearly what the pattern is. I've searched the net for French upholstery fabrics from the 1920s and quilt shops all over the place looking for something appropriate.The first fabric (0n the left below) was from the V&A, but was Victorian and, in retrospect, too pallid for Gert and Alice's taste. Below (right to left) are five fat quarters I have bought and rejected. The one on the right I found in a Eureka moment in a quilt shop in Cambridge (NZ not UK). It's obviously not the same fabric but it captures the spirit I want. It is on the cusp between Art Nouveau and Art Deco (the photo was taken in 1925). It's rich and shiny and thus will go with their Italian Renaissance furniture.
i gave up on the idea of making a slipcover --my one effort at that was a disaster (see below). So I put my little Bespaq chair in the microwave for about 20 seconds (thanks to the blogger whose name I can't remember who put that it her blog). I then pulled all the fabric off and used it for patterns for the new cover. This is as far as I got:
