Possible Clues:

• Sitting like a woman rider
• Ladies on backs of horses rode round ground -- disposed so?
• Way of riding a horse
• Teams count on the French - it'll be a rough ride without one of them for old horsey type
• Teams count on the French to be lady-like on the old hunt
• Teams go off riding in unorthodox manner
• Teams go off the way one may go up
• Chart-topping single of 1959, composed and played by Russ Conway
• A theologian in Leeds is excited to see ladies riding up like this
• Teams finally rejected rotten riding style