Based on what I see and hear, there are too many objections and barriers to an expanded Heathrow for this to be viable.
Given that the government seems to be determined to press on with the HS2 rail project which is going to link Heathrow with Birmigham, would it not make sense to use that to link Heathrow and Birmingham airports, which would take less than 40 minutes.
BHX handled less than 9 million pax last year and has an immediate capacity for double this figure. It has a big catchment area, with 50% of the population of the UK living within 2 hours drive and less by train if the links were adequate.
BHX could then become a serious hub and might even be a viable alternative to Boris' Thames Estuary Airport.