Yes, those trains to St Pancras are the easiest - far better than Gatwick express plus Tube if you have luggage. They do only run during the week though - highly annoying.
I second (third?) what Scumoftheroad said - I had a stand up row with a ticket goon man over which stations constituted London, and across London, and through London, and why the hell a return ticket from one part of London to another was not valid in St Pancras, last time I checked, also a part of London. Make sure you buy the right ticket, is what I'm basically saying!