Hello Jason , yes , tis an English bike tap , it comes apart and the cork washer (more of a cork tube) can be replaced easily by unscrewing it and sliding new one on . Should be able to get one from ebay probably , can over the pond anyway - see here
-https://www.ebay.co.uk/itm/SET-4-PETROL-TAP-CORKS-Genuine-Cork-Ewarts-ClassicBike-Triumph-dowty-Washers/223054012178?hash=item33ef0e1f12:g:1QcAAOSwHNtcd9ji
Or get replacement from Conrad , good luck , Ken