I don’t know if this was universal, but my old Building Society account used a passbook that you need to present when making a transaction (actually, they still offer them – I saw recent billboards where they’re trying to lure customers of a competitor that recently phased them out).
When you make a deposit or withdrawal, the transaction and updated balance is recorded in the book. That said, passbooks can get lost, so it must be possible to prove your ID and make a withdrawal without one (being issued a new one in the process), but they could insist you do that at your registered branch.
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