Its definitely a Matchless RS. The Model R Matchless first appeared for the 1926 season and was Matchless' first 250. It was steadily updated each year and the RS was a "sports" version of the same bike catalogued for the 1928 & 29 seasons. It looks a lot smarter than the original R but the engines are identical. Slowly Matchless developed this engine bringing out an OHV version, the R/3, in 1929, then adding dry sump lubrication in 1930.
This same 250 engine was steadily developed until WWII stopped production in 1940 and by then it was being used in AJS as well.
All prewar Matchless 250 are descended from the Model R but I don't know what year they started using them in AJS.
Cheers,