I remember that spoof well. It's on youtube. The actress you are thinking of is Joanna Lumley, famous in the 70s for playing Purdey in 'The New Avengers, and now something of a National Icon in the UK after starring in 'Absolutely Fabulous':Well Now you have to Catch up. They just announced the new Doctor today.
I find this humorous as a years ago There was a Dr. Who Parody called The Curse of Fatal Death where the Doctor is forced to Regenerate 4 times due to a running gag. Starting with Rowan Atkinson as a a 9th Doctor. and Landing on a 13th who bares a resemblance in Hair, eye and physical description although a bit more mature.
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