No need to buy tickets in advance for the Heathrow Express. You can get them on the train. If you buy them on the train they are 15 pounds each. If you buy them before the train they are 13. Cab ride to the Trafalgar (great hotel btw) should be between 10 & 15 pounds. Express and Taxi should be a heck of a lot quicker than the taxi, but it depends on which day you are going. Also, I've never been able to get a taxi or car to the airport for under 50 pounds. So, net-net, the Heathrow express will cost you a little less, but you should get there quicker. Again, depends on the day.