A blog on the Dr Who website said that the production team was recreating an iconic scene from a 1964 episode of the sci-fi drama. The Dalek Invasion of Earth saw the alien cyborgs arriving in London and passing the Palace of Westminster.
The BBC tweeted a picture of the original film.
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The entertainer was held for the murder of Stuart Lubbock, who was found dead in his swimming pool in 2001, but never charged.
Although the diamond was believed to be cut in the 19th Century, its history and how it arrived at the car boot sale is unknown.
The former entertainer, who was released from prison on Friday, is accused of indecently assaulting three women in the 70s and 80s.