Having consulted with our insurance rep the view is that all ride on machines need appropriate RTA insurance. Although it is a members only event other users of the site have access to areas machines will be in. The insurance provided as part of membership is Public Liability only.
Another possibility is that the mower is not a Barford attachment but a modified Merry Tiller or other make. I don’t recall seeing a rotary mower in any Barford leaflets.
If you want a manual for the ‘motor’ I assume you mean the engine, then you are looking for a Villiers Mk10 engine manual. If you want a manual for the machine it is a Colwood B. Dashwood Engineering were the makers.
Looking at the handlebar and trailer arrangement I would say that is a home made modification. As far as I am aware a trailer was not an option for the Colwood.
There is a trader that gets around the vintage shows who in addition to selling new tools also sells good quality old spanners. He has a very good knowledge of the older stuff. If I see him and can remember to ask I will.
I wonder if it would be worth asking the Tool and Trades History Society (TATHS)