Not among the short list of famous female drummers (which would include Shelia E, Karen Carpenter, Cindy Blackman Santana, Velvet Underground's Maureen Tucker, etc.) is the name of a female drummer to have a top ten hit her first time out: The Honeycombs' Honey Lantree.
She played drums on the worldwide 1964 hit "Have I the Right" and was prominently featured in the Honeycomb's TV and film appearances, as well the band's PR materials. Producer Joe Meek augmented her drum sound on their first hit with stomping feet and a tambourine smacked directly onto a mic, but there's no denying her driving beat really made the song.
While you're at it, check out the other great British bands on this time capsule of a rock music show, "Pop Gear": The Animals, Herman's Hermits, Peter and Gordon, The Spencer Davis Group and The Beatles. Find individual song videos on YouTube and watch the entire hour-long show for free on kanopy.