I passed my test in 1956, in an A40 Somerset. Not a big car, it had pretensions of being a 6 seater, able to accommodate three in the front, so had a remote control gear change beneath the steering column and an umbrella handle style hand brake beneath the dashboard. Neither made driving any easier. On the test I drove using hand signals, even though the car had semaphore indicators.
In 1958 I took my motorcycle test on a Cotton 250cc Villiers twin, again using hand signals, no choice in those days. I was sent round and round a city block while the examiner wandered about, until suddenly he sprang from behind a parked car, hand raised, for the emergency stop test. I suppose it's much the same today.
The Highway Code in the 1950s had a section for drivers of horse drawn vehicles. I don't think they needed a licence to do so, but it described how they should signal, using the whip.