That’s a question I’ve often wondered. My mum worked for the NHS in a ‘wages’ grade, weekly paid, from 1977, and was always paid by cheque; it went to bank transfer in about 1990.
Also in 1990 I worked for a large supermarket chain, paid weekly, and the default was to be paid in cash. This was ostensibly as it was the cheapest and safest way (for the supermarket) to get cash off the premises. Not so handy for you when you were collecting arrears / advance holiday pay when you could be walking out the door with £600 or so (worth about £1500 now).
I guess the answer to your question depends on the nature of the organisation. If it is a business without a lot of cash income, then it would have made sense to pay at least some staff in cash ‘out of the till’.
For BR, I wonder if there were different arrangements for those on weekly pay and/or at stations. In my nearly 30 years I’ve only ever been paid by bank transfer.