I have a 1948 British machine tool catalogue with an advert for Soag Machine Tools Ltd., London. Unfortunately their advert says nothing helpful! However, elsewhere in the catalogue they are listed as importers/agents for the following brands:
Progres lathes, made in Belgium.
Gilly horizontal boring, drilling, milling machines, made by Forges de Gilly, Belgium.
I am guessing from this and other bits I have found that this company were agents, not manufacturers. Lathes.co.uk mentions them under "Hogarth" and "Accura" lathes and also "Simplex" lathes as being sellers, probably getting their choice of name put on the castings.
I see there is a Soag company still existing in the UK, they say they have many years experience supplying, repairing etc. machine tools.
CNC Machine Tools | Aerospace, Automotive, Medical - SOAG
That lever to the right of the Norton gearbox looks unusual, as does the lever below in the base casting. Features like this may help to narrow down the maker (or it might be Simplex USA).