Beg to differ Laurel, tickets for Mousetrap are for sale at the 1/2 Ticket booth. Have been for years. Click on the link in my previous post and you'll see they are listed.
Debra wish I knew a way you could get cheap tickets in advance but I don't. The Ticket Booth in Leicester Square opens at 10am Monday thru Saturday and at a 11am on Sunday. If your schedule has flexibility you could visit during the day and purchase tickets for that evening. Maybe go there first thing, get your tickets and then off to explore other parts of London? Tickets into your money belt for safe keeping! FYI the National Gallery and St. Martin's in The Field in Trafalgar Square as well as Covent Garden are both within easy walking distance of the Leicester Square. Might you consider breakfast at the Cafe in the Courtyard behind St. Martin's then a stroll over to the ticket booth?
Lastly, as I also noted in a previous post this is a great place to enjoy a play, http://www.shakespearesglobe.com. Can book in advance and pick up at will call. Not saying it's cheap, unless you wish to stand during the entire performance. Merely saying it's another theatre option.
Great city to enjoy. Have a wonderful visit!