And Lamsons started off making the other kind of cash carrier, with a little carriage running along wires. I have a vague recollection of seeing one of those systems, most likely at Gamages (where there certainly was one) or perhaps Hamleys. They were obviously the kind of London shops a little boy would be taken to in the 1950s.
I also remember the tubes, which certainly were used in Bentalls in Ealing. All of those 50s ones would be operating the original method, where the receipt form and money (or cheque) would get sent to the cashiers' office, and the signed and/or stamped receipt and change were sent back. In between, if wrapping the item didn't take long, there could be an awkward gap to fill.
At Tesco, initially it was used to reduce the cash in tills by sending large notes over the maximum float limit with a slip printed by the till. With people using cards and some taking cashback, I guess that at some more recent time tills may have even started to run short of cash!
I'm sure there are a lot more examples of mechanical forerunners of gadgets that since became electrical, electronic, digital, and now virtual. My favourite remains the mechanical analogue computer.
And cash carriers (aka cash railways) of all kinds, like everything else in this world, have
their own web site. This includes a few bits of info about the railways' use of such things, e.g. at Euston and Liverpool Street stations, or the Great Western Hotel at Paddington.