Good question and welcome to the forum.
Webley never made the cases they marketed during the late 1930s and early 1950s. The cases are believed to have been made by Brady, who were a well established maker of Motor cases for shotguns and pistols, as has been pointed out.
The Service cases were made in three grades, the first two of which were constructed from canvas and leather. The third was made mainly of leather and while examples of the first two occasionally come up for sale, the leather case is very rare.
I was shown a leather case once, whose owner believes it to be original as it 'looks' right but as it is the only one known, it is hard to be 100% sure.
John
Currently looking for Baikal Makarov pistols with the following prefixes to the serial number: 98, T01, T09, T21, T22
Prefer boxed or cased but will consider loose examples too.