The study, published today, says that the "first best solution" is to build four new parallel runways, in two sets of pairs, immediately to the west of the existing Heathrow Airport site.
"These would run above the M25 and Wraysbury reservoir," the report says. "The Poyle industrial estate and a relatively limited amount of housing would need to be demolished."
The study says that moving the airport west would reduce noise over west London, "since the planes will be higher over any given place". But it proposes to "reinforce this noise reduction" by banning the noisiest planes.
The report says that because the proposal would reuse existing terminals and infrastructure, the cost of the scheme would be "far lower" than Lord Foster’s proposed Thames Estuary airport.
It says that around 700 properties would need to be demolished compared to the 1,400 that would need to go to make way for the estuary airport.
If a new four runway airport at Heathrow proves politically unfeasible, the report recommends that a four runway airport at Luton would be the next best option.
But it adds: "This approach is not as good as Heathrow because it would require the closure of Heathrow to be viable, and of Stansted on air traffic control grounds. As a result, the increase in capacity is smaller, and a second runway at Gatwick would be needed to cope with leisure traffic displaced from Stansted."
Leunig said: "We can and should expand aviation capacity in the South East. Doing so will send a much needed signal to people that Britain is open for business.
"It is possible to expand Heathrow in such a way that it cements itself as Europe’s number one hub, while significantly reducing the noise nuisance over west London.
"A four runway airport would be straightforward to construct and relatively low-cost by the standards of hub airports. It causes the lowest level of disruption to the wider economy of any likely airport expansion scenario."
Meanwhile, London mayor Boris Johnson has called on the government to accelerate work to deliver a new hub airport in the South East.
In a speech yesterday, he said: ""The government programme to address the looming aviation capacity crunch in the UK is far too slow and I am hugely concerned that their intended timetable sets a course for economic catastrophe.
"This continued inertia is being fully exploited by our European rivals who already possess mega hub airports that they intend to use to erode our advantage."
Bigger and quieter: the right answer for aviation is available here.