I work at LHR - behind the scenes it is a maintenance nightmare and the subject of some serious underinvestment in favour of prestige projects. T1 was mothballed on 29th June and will not be demolished until 2019 because HAL have run out of cash (they overspent on the new T2 by £2 billion). T4 has comfortably exceeded it's design life of 25 years and is falling apart (T1 was in a better material condition IMHO) but will only receive a facelift because, again, there is no money to rebuild.
The Government do not want to build a third runway at LHR, but they could probably get away with extending the northern runway and getting a new runway built at LGW too. Semantics is the key to this and an extension at LHR is not a new build - I suspect that Zac Goldsmith, Theresa May, Boris Johnson, Philip Hammond et al could just about live with this and it would get Cameron off the hook with BA, HAL and the CBI...