I must admit I have never heard of plum cider, it sounds fascinating.

I reckon your recipe only specifies Warwickshire Drooper because it used to be quite widely grown as a processing plum, and therefore would have been readily available to anyone looking to make plum cider in the English Midlands say 50 years ago. You could probably use any other European culinary plum, or damson, or possibly a mirabelle. Also, check the pedigree of some of the modern plum varieties coming out of US and Canadian research stations, because in some cases they may have been developed from some of the older European "prune" varieties. Unlike Japanese plums, most European plums and some gages are also excellent for cooking, and therefore probably suitable for you.