Hi-speed rail does wonders for flights to New York.
Actually, couldn't this exacerbate the problem of congestion at Heathrow? Without knowing any of the details of pax distribution, it occurs to me that making it easier to get to LHR, especially from places that don't have any or many flights to LHR, will direct MORE traffic to LHR that might have gone elsewhere-- might have connected through another airport. For example, take someone going from MAN or BHX to USA. If it's easier to get to LHR by train and jump on a nonstop flight from there, why not do that in preference to a connection elsewhere in the UK or on the Continent or in the US?