The Clink Prison Museum: At this location, situated in Southwark, it is said that J.K Rowling's herself got her inspiration for the Death Eaters. How cool is that? And it is relatively inexpensive for a London attraction. At only 7.50 pounds per person, you cannot beat the value. It is built on the site of the original clink prison. It is also right across the way from the other place that should have mention...
The Anchor Pub: This historic and charming place is said to be one of the most haunted pubs in London, at least this was according to our tour guide. It is said to be haunted by a dog who lost its tail and its master by a presser gang in the 1700's. They say at closing time it comes back to sniff around. I am not sure if a dog haunting constitutes the most haunted pub in your book, but there are lists and lists of haunted pubs in London. I think that at least a half day dedicated to checking out all of the haunted pubs (with or without a cocktail) would be a great way to explore some of the English history, sample unique food, and enjoy a day pub crawling.
http://www.clink.co.uk/index.html