Whilst that was an original estimate several years before the bid formally took place, Parliament agreed to a budget of £5.3B for the games, an extra £2.7B contingency, "security and policing costs of £600 million, VAT of £800 million and elite sport and Paralympic funding of nearly £400 million" [0]. £2B for actually staging the games is covered by sponsorship etc.

As the agreed cost before the bid was finalised, this is really rather close to the $18B figure the cited Parliamentary report comes up with.

[0] http://en.wikipedia.org/wiki/2012_Summer_Olympics#Financing