Although Wilson Brothers (Leeds) was in business in 1937 it was incorporated as a limited company in 1960 but was dissolved in 1996 so the reason you can't find anything is because the company no longer exists.
Google the name and you will find this from a quiz run by the Woodwork Uk site in 2007.
"Q. A Yorkshire firm who manufactured woodworking machinery from the 1860s we were also well-known for our railway engines and other engineering products. Who were we and where were we from?
A. The firm was Wilson Brothers (Leeds) Ltd who were established in 1862 and survived until the 1990s. The firm also known for it's manufacture of saw mills, complete with both stationary steam engines as well as railway shunting locomotives, although they do tend to turn up more in places like Australia or New Zealand than the UK. Wilsons arre reputed to have supplied contractors engines in the UK as well.
Oddly, in the late 1950s and early 1960s, Wilson's was a progressive firm with many more modern designs than market leaders Wadkin and White (for example they were an early adopter of fabricated steel frame bandsaws some 10 years before Wadkin followed their lead)"
