The Lady Shellington did her show, "One Fine Day: The Groovy Girls of the '60s." For what it's worth, she is one groovy girl herself. (Besides being a wonderful singer, she's also a terrific screenwriters, and so -- unlike most cabaret acts -- writes all of her own material. Just just the patter, but the song parodies which are mixed in among her straight-forward songs.)
Here's a video of one of Shelly's parodies, "The Middle Age of Aquarius."