I remember my father going away and putting a lock on the rotary dial phone - this meant you could only dial 999 I think - but my brother quickly showed him you could 'tap' out the number in the number in the way that you describe. I'm not sure who my dad was locking out - maybe we had lodgers at the time?
Later we bought a 'fancy' answerphone that you could retrieve, save and delete messages from a remote phone by playing a tone down the line. It came with a special tone generating battery operated touchpad you could hold to a receiver to play a tone down the phone, as plenty of phones were not touch tone yet.
I remember you could also use that to dial numbers some how - later a friend had a Casio watch that could also generate and 'dial' numbers for you. I tried from a payphone but it wouldn't work for me.