I did have a look at the various Lympne trials aircraft over the years, and as Allan Lupton says, its none of them. I can't find pictures of the unfinished RAE Scirocco, which wasn't ready in time though, and is recorded as 'never completed'.
I also had a look for Vauville designs which was the French equivalent of the Lympne Trials, but no luck their either.
Fauteil Volant, the idea of it being a large model is interesting, but IMHO unlikely. Colonel CE Bowden was the most well known power model flyer at the time, and his biplane 'Kanga' had 'only' a 28cc Wall engine. Anything larger would be unlikely to have gone unnoticed by the modelling press. Your list of unregistered aircraft provided a fascinating hour of education. The Worsell Monoplane listed as being at Sevenoaks, looked like it might be a contender, but it was made from Boulton and Paul P.9 bits, which look too large and the wrong shape.
The cutouts in the wing leading edge roots of the mystery aeroplane are a significant feature, plus the very substantial and wide track undercarriage. I do wonder if its is a 'bitsa', but bitsa what?
Buying the V-Twin engine must have been a substantial investment, on a par with buying a Rotax microlight engine these days, which suggest it must have been a serious project, especially as it is claimed to have flown on several occasions.
Do please keep searching. The answer must be out there somewhere!