I think it will be possibile to snatch a last-minute tickets. When I was in London last April, I wanted badly to go and see Measure for Measure. It was plying only for few days and all sold out, but I went on the Barbican site on the day of performance and there were 2 or 3 return tickets. My friend spent an hour pressing "refresh" button next day, but eventually she got a ticket, as well.