Patent searches have actually proved the least helpful, principally because there has only ever been one patent for this design of air pistol, undoubtedly the most ubiquitous airgun design ever introduced. That patent, the brainchild of inventive genius H.M. Quackenbush, dates back to 1876. Experts have since trawled the US, UK and German patent literature for any related 20th century patents and regrettably (but not surprisingly) nothing has been found which relates in any way to these 1930's pistols.

Thanks also for the other suggestions but unfortunately I have to say that all these ideas have already been followed up quite diligently. We have to keep in mind that despite the large numbers of these pistols made, their period of manufacture was quite narrow (1931 to 1939) and so it has been relatively straightforward to focus any particular searches. The principal British sporting goods magazine, Sporting Goods Review, which has always provided a wealth of information about airguns new to the UK trade, has been closely scrutinised by noted researchers John Atkins and Tony Williams, with nothing of relevance being found. As these guns were not legally classifiable as toys they never appeared in toy catalogues.
Usually in these circumstances the best hope is for an old employee to come forward with some first hand insight, but given the 80 or so years that have now elapsed this is increasingly unlikely. I suppose that it was the relative insignificance of these guns, combined with the political situation in the pre-war years if there was a German connection, that was responsible for the lack of any documented information about their manufacture and distribution. We just need a lucky break!