IIRC, which is not guaranteed, there is a thread somewhere about a collection of vehicles at Crystal Palace or Neasden, including a Mk VII and maybe A7V. They were all scrapped because of lack of space.
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The IWM didn't move to Lambeth until 1936 and the WW1 exhibits were scrapped long before that. Between 1924 and 1936 the collection was in a space in the Imperial Institute in South Kensington.
Just as well really, because the Crystal Palace burnt down in 1936, so those exhibits that do survive would have been lost completely.