Let me start by saying I went here last year and it was creepy AF. I love Hampton Court Palace, it's super interesting and absolutely beautiful, but late at night it is pretty damn creepy. The tour is super interesting if you like your history dark, and you'll get to see the exact place where the reported ghost that haunts the castle likes to linger (see video). The bedrooms are the scariest bit though, and there's even a part of the tour where you have walk down a very dark corridor alone, so it's not for the faint-hearted!
Tours run on selected dates (including Oct 31st) till February and you can get more info and tickets here.