The project will go ahead, but there is an election in the UK in June and given the controversial nature of the project, the government will not make it decision public until after this. Once the go ahead is given, the project should take about 4-5 years to complete.
BA's CEO has been in the news recently to complain that it has taken nearly 20 years from the time the terminal was first mooted, to the time it will come into being. It would be difficult to argue with this. BA would also LOVE to have a third runway at LHR, although BAA has invited the inquiry chairman, Sir Roy Vandermeer to exclude that possibility permenantly. (I think/hope this is just a trick; I think BAA would also like a new runway). It will be interesting to see what the report finds; it is also expected to clamp down on night flying.
The SE of England badly needs a third runway and I sincerely hope this is built at or sufficiently near LHR (ie Northolt) to make it work as a satellite for LHR. It needn't be as long as LHR's runways, but a runway of about 7,000' would relieve a lot of pressure from LHR by being able to take aircraft of up to 321/757 size and even landings by aircraft up to 777 size - even 747s in dry conditions. Such a runway could take around 110,000 movements a year.