Why not try:

MATCHLESS GB0/AJS MODEL 18

In1959, like BSA, AMC ditched their magneto and generator set up for an alternator/points arrangement. Onthese singles this meant a significant change in the way the engine looked, losing the attractive drive chain case to the magneto infavour of a cleaner, but somehow duller, more homogenised appearance. Similar to the BSA in the way it performs, possibly a little less fine handling, though many would dispute this, the AMC singles are a good alternative and tend to come in cheaper.

NORTONES2

You'll pay for the name with a Norton, but you'll stay for the ride. This long stroke single was reliable, easy to look after and a long-standing design. It went through similar design changes through the 1940s and 50s, ending up going into a slimline Featherbed frame. They were, according to those that knowabout these things, better intheir preFeatherbed versions. The last ES2, the Mk2, is a Matchless with Norton badges and while not a bad bike, isn't really the same thing.

VELOCETTE MSS

An idiosyncratic, delightful 500 single from Velocette. Stylish as heck, Englis has tuppence, the postwar MSS arrived in 1954 with the same frame as the Velocette MACT. he swing arm version was the longest lasting single from the classic period. It features all of Velocette's more unusual features, especially inthe drivetrain department. You'll need to have either a considerable aptitude for mechanics, and engineering skills willbe handy too, or have money and/or a good friend with those skills. But my goodness, they are lovely to ride.