Wonderful pickups, Rob, especially (to my mind) that Bank Dollar, which would fit nicely into my own set. I know there are a minimum of five varieties of the obverse and three reverses, so you'll need to dig a bit into ESC to nail that down.
As for the Maundy Fee, it's my understanding that those were paid (in envelopes like yours) to the Lord High Almoner as compensation for his (exclusively male back then, of course) arranging, assembling, and stage-managing the Maundy ceremonies for the monarch. Long-standing tradition, if not law, required that his costs be covered by payment in Maundy money itself. I first encountered this practice in print perhaps forty years ago and I've questioned or "doubted" the published mintage/distribution figures ever since, because where have we ever been told how many sets went to the Lord High Almoner (and staff, possibly) to cover their costs?
The upside of that history is that once you've identified the Lord High Almoner for 1940, you'll know where your set's provenance began. It was a role often played by the Archbishop of Canterbury, as I understand it, who sometimes actually stood in for the reigning king and/or queen when they were unable to make it for the actual distribution to the poor.
Great stuff!
"If everything seems to be under control, you're just not going fast enough."
--- Mario Andretti