There are many variations on this game Freddy. On 'playground duty' for decades as a teacher, in Edinburgh, Glasgow and Norwich (1960's onwards), I watched it being played in several ways.

In Norfolk it's fairly similar and is called Hot Chocolate. But no words are spoken, the children creep up and the person who has turned their back turns round suddenly. If anyone is caught moving they go to the back and start again.

As a child in the late fifties (W London) we played Mr Crocodile ("Please Mr Crocodile, may we cross your golden river?" "Only if you're wearing blue, take two steps..." and so on)

I also played Mr Wolf (not Fox). But that, as you say, was a bit different. No-one moved, but Mr Wolf, with his back turned away, answered with different times, until he said, "Twelve o'clock! Time for my dinner!" and grabbed someone to 'eat' them.