I don"t know what your budget is, but I would definitely get the train if you can afford it. If you plan to arrive in plenty of time youwill be relaxed and refreshed, ready for concentrating over a long period. Go by car and with the sun pounding through the windows, plenty of speed restrictions on the M1 with average speed checks, traffic when you get to London, hassle of finding the Vic and then somewhere to park, you"re likely to be relatively hot under the collar and that"s not ideal preparation.
Accommodation is not going to be cheap. There are some budget hotels fairly near Baker Street tube, which is handy for the Vic by tube and when they stop running and you are looking at a taxi, the area is nearer than anywhere else in London that has budget hotels that I know of: others may know better.
A tip - if you are staying at a budget hotel in London, pack a bath plug just in case your room has a bath, because for some reason the plugs in those places go missing!
