Rudge combo with mystery two stroke

Two late twenties bikes on tour. The combo is easy to recognise as a four valve four speed Rudge, really not sure what the other bike is though. Anyone got any ideas?

Touring twenties style. Rudge combo, a pair of dogs
and a mystery two stroke.

postscript: Thanks to the comment from 'anonymous' who has pointed out that the two-stroke is in fact a Dunelt.