The site owner has put an easy to use search facility to information published quarterly by DVLA regarding the number of vehicles currently taxed and SORNed.
It isn't infallible, as vehicles which were SORNed prior to the change which made SORN a requirement if you were not taxed or insured are not shown, and the vehicle model shown on the V5C may not include all the model information correctly i.e. there isn't a category for "MZ TS250" or "TS 250/1", but these models will be included in "MZ Model Missing" section, which shows 1300 taxed & 3400 SORNed.
Mrs B has a BMW R65LS - never a popular model, but according to the site there are currently only 14 taxed & 55 on SORN in the UK. Not many to choose from if you were looking for one !