The old system (BACS) has been electronic since 1983, or possibly even 1968 when it was introduced. (Wikipedia is unclear, it seems transactions were recorded on magnetic tape for the first 15 years, before using phone lines.) It slowly replaces the paper based system: cheques.

The 2-3 days got the old system will have been a limitation of batch based computer processing from that time, and maybe moving the magnetic tapes around.