The basement bar is named "Old Mary's" to commemmorate a maid named Mary who was murdered by Lady Craven when she found out that she was having an affair with her husband. Mary's spectre has been seen here but details are lacking. There is also said to be a phantom coachman in the pub; he lived in the stables where the cellar bar is now.
Update 4/5/22: I emailed the pub asking about any recent phenomena and Rebecca Whittome, the General Manager replied saying, "We have experienced some odd things here at the Mitre, we are more known for our basement ghost 'old mary' our cocktail bar is named after her, but there have been strange things happening on all 5 floors." Soon afterwards we spoke on the phone and she gave me a list of some of the phenomena that have occurred while she has been at the pub (two years). In the scullery area, she talked of black shadows, seen in the peripheral vision, and she has also been touched down there, including fingers on the back. On one occasion, she went down there on an errand, but forgetting why she had come, asked herself out loud, "Am I supposed to be here?" and was answered by a male voice behind her saying, "Yes!" In the bar area in the basement, her deputy caught a quick glimpse of a man resembling a highwayman. On the ground floor, a man described as "gloomy" and "glum" and with dark, shaggy hair, has been seen sat opposite the fireplace. He was seen briefly, and then he was gone. He was described as being in his 30s, and wearing a 1960s style suit. It is also in this area that glasses have been forcibly pushed from table tops onto the floor. On the top floor is the flat reserved for managers, and very recently her son, who was nearly 12 saw a white cloud, like "a fog" go into the bathroom but it had gone when he entered. Rebecca also something similar in the staff flat below which she as first thought was cigarette smoke. It was also in this bottom flat that she and her husband have seen the ghost of a child. Rebecca described one incident when she was asleep and felt someone touching her; she woke and saw that it was a 5 or 6 year old boy. Incidentally, Rebecca told me that the back story was that Mary had been pushed down the stairs.
Link: The Londonist
Link: Shady Old Lady
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