The correct music is Benny Goodman and his band playing swing music. The jitterbug or the "jive" is all the rage.
Frank Sinatra is only a skinny American kid. His music hasn't reached Britain yet, and cheek to cheek is for slow dances only near the end of the night.
Chubby Checker and the Twist is classic rock and roll from the late 1950's. your kids will love it.
Rudy Vallee and the Foxtrot are from the 1920's. Your parents danced to this when they were young.