A Churchill O/U was sold at the recent Rock Island auction. It was a pre WW11 gun built in 1925.
This doesn't help to answer how many post war O/U were built by Churchill but it is interesting to see as any Churchill O/U is rather rare.
I did a quick search of a couple of gun auction catalogs and did see a modern day Churchill for auction.
Perhaps, you could contact Churchill and persuade them to do a search of their records.