An ambitious plan to build a high-speed rail line north of London via Heathrow ^ relieving the pressure for a third runway at the airport ^ is being drawn up by Arup , the influential engineering firm (link below.)
http://business.timesonline.co.uk/tol/business/industry_sectors/transport/article2982649.eceArup^s plan would see the Channel Tunnel line extended west , parallel with the Great Western line. After Heathrow , trains would turn north along the alignment of the Chiltern line , running to Birmingham and Scotland.