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Looking at the Sunbeams on Ebay I was shocked by the prices - I had to go and check that the £ sterling hadn't collapsed to 100 to the dollar!
Particularly outstanding was the one with the rusted out chaincase, which had been stripped various essential parts (Cranks, BB) and appears to have been sold for £260!
As it happens the photo in that ad., showing the chaincase rust hole, shows the reason why a chaincase could not be fitted to my machine. Inside that case there can be seen the 'strut' which forms the right hand chainstay on these frames (mine has a conventional RH chainstay). If you have a Sunbeam with a chaincase you can't use the bike without it because it forms part of the frame, but equally, you couldn't add a chaincase to my frame.
These chaincase/strut frames are not rigid, and you can hear the case flexing if you get out of the saddle to climb.
I have most of a 'chaincase' Sunbeam in a shed. It's a 21" gents frame with 26 x 1 and 3/8" wheels including 3 speed hub. I think it's from the BSA period. If anyone wants this, I'd be pleased to see the back of it for a modest donation to the forum. Collection only from NW10.
Im not sure about Oxford but im sure there would have been some second glances in Dartford and its environs.
Would you consider fitting a full on chaincase, Lighter and arguably more practical without it, however looking at Sunbeam Roasters on Ebay they do look cool with the chaincase.
Good luck with the riding.