Is there anything that compels T1 to be demolished, apart from future intended usage of the land it occupies ? It's going to cost money to knock it down, and I'm left wondering if demolishing T1 can be deferred for a couple of years until LHR's traffic recovers enough that there is confidence new building work on the site of T1 will have a sufficiently high rate of return.
Perhaps money should not be spent on flattening what is essentially a disused building on a brownfield site in west London until somebody can come up with a business plan to make proper money from it