I took a photo from the car park at Myddelton House, but it was a very grey day and the main building practically vanished into the overcast background! Things are a little more advanced than in the aerial view Vedi posted, though.
In December, there was a job advert on the OS for an academy kit assistant and in the info it said "Initially, for the first four/five months of employment the successful candidate will be based at the Club’s current training ground in Chigwell, moving to the new training ground in Enfield in May/June 2012"
Guess that is the answer for the expected move-in, provided all goes to plan!
I'm not certain, because I've never been there, but as most of it is open space, I suspect that the local planning authority will want it to remain similarly open, i.e., any major new development would be unlikely to get planning consent.
And I believe I read that THFC doesn't actually own the land. Not certain of that, either.