I'm not sure if Waddington's would be the only company, at the time, who could print small details on fine fabrics. The technology had been around for some time, but was fairly involved and relatgively expensive, where consistent, accurate detail was required.
I now live in Macclesfield, which was the center of the European silk industry, at the end of the 'Silk Road' from Asia, and some of the older, original 'home grown' residents I know, have told me about the production of silk for parachutes being a major production requirement during WW2, even allowing for the introduction of the Du Pont 'Nylon' fabrics which eventually replaced silk. I've also heard mention of silk map production, and a large print works in the town, now closed, might have been printing these also, according to the locals.