Many of these workers would find themselves and their jobs well and truly caught up in The Second World War in less than ten years, with this air mail pilot and his trusty aeroplane both almost certainly being swept off into the RAF, though perhaps he might have found himself part of the Army Postal Services, which was pretty much run by the Royal Engineers (Postal Section).
I think the way the cards are drawn definitely foretells the change in the air with its shadows, and its dark backgrounds, and its use of torchlight illumination.
We will never know who these men were modelled on, because nobody thought those sort of facts worth recording, and the same is true for most cards of non-celebrities, which is a very great shame.
This is a most attractive set, and you can see all of the cards at https://buttes-chaumont.blogspot.com/2013/12/whilst-we-sleep-with-typhoo-tea.html
If you have pinterest you can also see them at https://www.pinterest.co.uk/gene1897/whilst-we-sleep-typhoo-tea-cards/ but I can only look so far before they block me for not having an account.
Typhoo Tea is still going, dare I say it, "strong" (or is that just the way I make it?) and it has a website, not just to sell its wares, though this is of course the primary purpose of most websites. It also includes the story of how the business came to exist, at https://typhoo.co.uk/about-us/great-british-tea-since-1903/ - during which it even mentions that from 1906 John Sumner included "circulars .... and picture cards ... inside the packets. These are still collectable to this day!"