Mk1 S cars used the 23D4 in 2 versions with service Nos 40819B and 40819H. These have slightly different advance curves to suit the 2 different standard camshafts used. The advance curve is for 100 octane leaded fuel and both required a retardation of the static timing to stop pinging at low engine speeds when 97 octane leaded fuel was used. It was pretty common to use aviation fuel or fuel additives such as benzine to boost the octane rating of 97 octane fuel back up to 100+ octane.
The first type 40819B is for the AEG148 cam used in 970, 1071 and 1275 cars up to engine No 9FSAY 40006. The second type is for 1275 cars using the AEG510 cam. The only difference is the second version has slightly more advance at low speed (1 to 2 deg?) to suit the AEG510 cam. The advance curve tolerances for both versions overlap each other so in practice it probably doesn't matter which one you use and in any case after 40+ years the advance curve in either is probably not accurate.
The OZ MK2 S and Clubman GT use the 29D4 distributor marked AYG0175. Later GT distributors have only a Lucas service No (IIRC 62941090). These are Australia only Lucas designs (also came in 29D6 and 29D8 versions) and parts are scarce.
Hope this helps
RonR