I'm a long way off over in in Cambridge....
The bike is actually in Kent at the SOF Presidents shed at the moment, having a full engine rebuild. If anyone tries to persuade you to have the conversion to modern oils, by removing the sump filter and inserting a paper car type element, just punch him. I allowed myself to be persuaded, by a supposed 'Sunbeam Specialist' repair and restoration company in Hampshire. What then happens is that the nice shiny modern 20/50 oil running through the motor cleans 65 years worth of crud off the inside of the engine, where it had been sitting harmlessly as it was designed to do.
Then, modern oils suspend crud in them to be got rid of during oil changes, unlike the Sunbeams original design which dumped it on the sump filter, it turned said shiny 20/50 into 3 and a half pints of grinding paste..... Cue new main bearings, shells, etc, total engine rebuild within 20 miles of getting it back.... He also refitted the dynamo incorrectly, causing the armature to touch the field coils, burning it out. Luckily, it cut out because of the dynamo failing, or Id have scrapped the engine on the same ride.... If the engine had been clean it would have worked, but you cant convert an old engine, as it pisses the thinner oil out of everywhere! He also denied any responsibility for any damage to the engine. Avoid at all costs.
I wouldn't worry too much about the conditions in your shed, one thing ive realised over the years, Brit Iron is tough and laughs at just about any weather conditions.