There are limited options when it comes to trying to secure tickets to sold out shows.
Some theatres provide a number of tickets for purchase on the day of the show only and usually in person from the box office (notably the National Theatre do this, from 10am on the day of performance).
You can also try queuing for returns at the box office – usually by arriving either at a specified time or a few hours before the show, in case any tickets have been returned to the box office.
It’s worth saying that it is NEVER ever worth buying tickets from a ticket tout. You will often pay many times the face value of the ticket and often for inferior seats.
It is also worth saying that most shows are not sold out and you can usually secure tickets for the West End show of your choice. The actual box office of the theatre, and well-respected ticket agencies such as Encore Tickets – who provide ticketing for WestEndTheatre.com – have good allocations of seats at all prices.