I think I did as a child at school!!

we had a string up, a shuttlecock, wooden bats (larger than a table tennis bat).
The game basically was hitting the shuttle to each other over the string and counting how many continuous hits we could do without the shuttle falling down.

It somewhat fits a description of the game.

That was a very long time ago in a very small, English traditional school........

I think I've played something like that when I was young.
I never knew it had a name. :p