I am trying to remember when they started to be replaced by push-button 'phones.
Was it in the 1980s or 90s, as electronic telephone exchanges replaced the electro-mechanical Strowger switching that had already long replaced manual exchanges? (The move to electronic exchange circuits was already underway in the early-1970s.)
The Post Office Telephones, as what became British Telecommunications / British Telecomm / BT, was, introduced a version called the "Trimphone" in the late-1960s. This as a dial telephone with a sleek, streamlined case, and luminous dial. Later versions had push-buttons instead. It used an electronic warble tone rather than pair of bells struck by a central, vibrating hammer; but still giving the distinctive double-burst "ringing".
The luminosity was by a low-level radioactive element, tritium; eventually abandoned over safety concerns.