Don't expand Heathrow - extend Eurostar to it

I was struck by the press release from Norman Baker. I would think one solution to at least part of the problem is not to expand Heathrow, but to extend Eurostar to it! Or am I being naive?

Transfer passengers increasingly crowding already congested Heathrow - Baker
Nearly a third of all passengers at Heathrow, Britain's most congested airport, are expected to be travellers stopping only to change planes by 2010, the Liberal Democrats have found.
The figures, obtained in a Parliamentary Answer, show that the number of people switching from one international flight to another at Heathrow is forecast to rise to 31% by 2010.
Commenting, Liberal Democrat Shadow Transport Secretary, Norman Baker said:
"These are devastating figures which show that the third runway, for all its massive cost and environmental damage, is being built to help international transfer passengers who never even leave the airport.
"If the number were reduced, there would be no need for a new runway and far more space at Heathrow for people starting their journey in London.
"With ever-increasing demand on Heathrow, we don?t need transfer passengers to make routes viable. They are there simply to satisfy the greed of BA and BAA."