Had them too, and there was an indent in the bottom of the balls where the string was knotted. I made the string shorter and it made it much easier, and could play with them for hours.
But I knew them as ‘ker-nockers.’ Many bruised wrists and hands and had them til they fell down the drain in the street while playing with them. 
We also had ‘French skipping.’ A round of elastic that went round two peoples ankles, calves, knees or thighs. You had to jump in/out of the elastics without treading on it.
1,2,3,4 out in on out twist off… 🫣😂
The other thing we had was a tennis ball in a stocking! Played it standing with your back to the wall, and swung it so it hit to the left/right of you or above your head, or below your torso (between your knees) I don’t remember the song to that though.
And street skipping. Many a time the Mums in the street would turn a giant skipping rope for 10 or more kids at a time, so we could all jump rope together. They even got involved and had a skip themselves, while all of us kids looked on in awe!
We lived in a cul de sac so everyone knew each other, and there was always someone to play with. We was also on a hill, and before skateboards, we used to get our yearly Christmas Annual and balance it on just one old metal rollerskate. We’d sit on it, knees bent up and feet flat on the book, and zoom down the hill, where we’d wear out our shoes or plimsoles by using them as brakes.
Happy memories right there… 