Azizi,
I have no recent information on UK happenings. I'm talking about the 1950s / early 60s. The Grand Old Duke of York would usually be danced at parties (Christmas, Halloween, etc)organised for the kids by parents in small communities and villages. TV wasn't that big yet. We would do other "dances" like the Hokey Cokey (You put your left hand in... that's what it's all about!) aka in the US as the Hokey Pokey. Other kids' "dances (or games)" like "I sent a letter to my love", "The farmer's in his dell", "Musical Chairs" and "Pass the Parcel" would also be played.
There usually wasn't a band or any kind of recorded music - just a piano player and we all sang the words of the song as we participated in the activity.
I don't recall there being any problem with boys and girls of 8-14 years interacting with each other. It seemed like a natural activity encouraged by our parents.