Cecilia, that sought of information is going to be very difficult to locate. One could spend ages in TNA going through loads of files and come up with virtually nothing. Obviously I don’t have the definitive answer but I doubt it very much that it had come back from France. Why would it, the British countryside was littered with army camps and PoW camps each with masses of huts. It is more likely that huts erected in France post WWI were used as firewood I am afraid. I note that Sutton Coldfield (Sutton Park Camp) was a WWI camp for ‘Birmingham Pals’ for example.
The only way you are going to find out I guess is to locate the sales (auction) brochure, but finding that might be difficult, but one could make a start with the local paper as War Office auctions would have been well advertised in editions leading up to the sale.
I presume it is an Armstrong timber hut that you are referring to and not a Nissen hut? Do you have any pictures?