When people used cheques their sort-code was revealed to anyone who handled that cheque - that's what the bank explained to me re providing bank account details.
Aww I'm nostalgic for cheques now!
Remember when you used to go into the branch to "cash a cheque" because there were no ATMs...
But again. Your sort code reveals only where you originally opened your bank account. (EG Natwest, London Rd Brighton.) It's hard to see what anyone's gonna get out of that - surely even the most crazed loon of a client isn't going to sit outside your home branch 8 hours a day, 5 days a week on the off chance that you'll pop in?
That said, I do use a secondary account for bank transfers, which is at a branch somewhere I haven't visited for 20 years. But that's more about ringfencing the funds so I can transfer them to my main account quickly in case of attempted chargebacks.