Comments so far:-
a) Definitely not a Rudge, but that said I’m not sure what it is. I’m usually pretty good with the type of bike that came to Australia, even c1930, but this one… I notice that one of the photos is labelled “BSA”, and in fact the frame looks very BSA. The sloping motor was also a BSA thing, but not this particular motor. All BSA slopers had the oil in the sump that was part of the crankcase at the front. Unless it’s a “special” (a late 1920s vertical BSA motor grafted into a BSA Sloper frame), then it’s not a BSA either. The problem is that I have a list of things that it isn’t!
b) so far opinions are that it is a Rudge, by the rear sprocket and sweep of the pipes, plus the primary chaincase and shape of the tank
c) The sloper has us all miffed and there is a good chance it could even be a home brew.
It is fairly unusual for a motorcycle engine to have exposed strengthening ribs but not so uncommon for a stationary engine to have extra strengthening added to cope with the higher loads
It is a twin port sloper that is sure and from the size of the pots I would think that it was 500cc or larger.
Again I do not think that it is a BSA the cases are the wrong shape, the strengthening ribs on the crank case is not usual on BSA's & the primary chaincase is also an unfamiliar profile.
Sloping engines were all the rage from mid 20's till WWII and just about every marque had a sloper or two in their range. I am not a motorcycling historian by any stretch of the imagination and what knowledge I have picked up over the years is specific to BSA and I seriously doubt that either was a Small Heath product. What I can say with 100% confidence is that it's not a Gold Star.