From "Modern Sporting Guns" by Christopher Austyn: "There is no legal minimum thickness for a shotgun barrel, although the British Gun Trade Association RECOMMEND 20 thousandths of an inch as a general minimum." (Emphasis the author's.)
As noted above, there are plenty of British game guns that left the maker with MBWT well under .035. As also noted above, the main issue with barrels (assuming good condition) as they approach .020 is what happens if you dent them. Likewise, the location of the thin spot is also important. Like Jeweler, I wouldn't be overly concerned with a gun slightly under .020 close to the muzzle. Pressure certainly wouldn't be an issue in that case.
