Granted they are not underground stations, but the briefest of glances at a London street guide revealed Freemans Road, Martins Close and Painters Road. None of these contains an apostrophe either. One just has to respond to this sort of thing down with the response: "Because it's so!"
Well Clearly it's a court owned by a bloke called Earl and a statement of fact about barons, I mean clearly a Baron would take a young lady out to dinner occasionally so one could say Barons court.
it should have an apostraphe. but it'll be for some historical reason that it hasn't got one (can't help you there, sorry). lots of other old places don't have apostraphes too.