Yes, the Sturmey Archer gears were crap, and three is no where enough for a bicycle.
Low gear is too high for steep hills, and high gear too low for any kind of speed - really pretty naff all together.
Mind you, I used to have a Rudge single gear bike in my teens, and I used to get round pretty well OK - including some VERY, VERY steep hills (I still have the scars from getting knocked off by a car on one VERY, VERY steep hill - but I did take the wing mirror off with my head - it was a Ford Granada).