Since about year 6 of the Londno Marathon, the DNS rate (allocated a place but did not start) has been fairly consistent at between 25 and 30%.
I'd agree with millsy that the race organisers can pretty much bank on about 25% not turning up to the start line. This equates to approx 35,000 starters out of 50,000 successful applicants. Not hugely surprising when you consider the london marathon is a very popular mass participation event, and many of the successful applicants will be first time marathoners or infrequent runners, so the injury rate will probably be quite high during training, as will be the "christ, i didn't expect it to be hard" rate. But once they've rocked up to the start line, that same demographic will feel compelled to complete the race, having raised money for charities and dressed up like Spongebob Squarepants, even if they have to walk the second half.