The Queen's long standing fandom for cult SF is one of my favourite things about her. Not just Doctor Who, but she famously casually defended the 1950s adaption of 1984 against parliament caution about the content.
Or as Nigel Kneale put it (heavily paraphrased): "One day, MPs and the press hate it, the repeat performance is off. Next day, the Queen loves, the press and MPs talk about what great TV it is, the repeat performance makes everyones career!"