Speaking to getwestlondon, CEO of the airport, John Holland-Kaye, said they are confident the plans are deliverable and show they have addressed the concerns of local residents.
Director of external relations, Nigel Milton, said: "As long as prime minister Theresa May and chancellor Philip Hammond are in government, we will get through to 2021 and start third runway construction."
Mr Milton said selecting Heathrow showed the prime minister's commitment to Brexit negotiations by keeping the country open for international trade.
The message from Heathrow comes as lawyers on behalf of Hillingdon Council gave a stark warning to the government in a letter on November 17 calling on it to force the airport to withdraw its application.
The 33-page letter, penned by solicitors Harrison Grant, argues the government's decision is unlawful because of the impacts on air quality and noise pollution.
Hillingdon, Richmond, Wandsworth and Windsor and Maidenhead Councils along with Greenpeace make up those who will be launching the challenge against the Tory government's decision to expand in west London.
Leader of Hillingdon Council, Ray Puddifoot , said last week: “I was in the High Court in March 2010 at the last JR [judicial review] on Heathrow expansion when the judge referred to the third runway plans as 'untenable in law and common sense'.
“Six years on it is unbelievable that the current government are promoting an expansion that is still untenable in law and common sense and it is simply not acceptable in this country.
“This is the first round of this legal challenge and whilst we should win by a knockout in the first round we are prepared for a long fight if necessary.”
During the Mayor's Question Time last week (Wednesday 16), Sadiq Khan also announced he will be backing the legal challenge against the third runway.
Watch Sadiq Khan at Mayor's Question Time announce his support for legal action
The legal challenge is just one of a string of events since May's decision at the end of October, the latest seeing 15 people charged for obstructing a highway near the M4 during a RiseUp! protest on Saturday (November 20).
A spokesman for the Department for Transport said in response to the legal challenge last week: "We believe the Heathrow Northwest Runway can be delivered in line with our obligations on air quality, with a suitable package of policy and mitigation measures.
“We are unable to comment on the detail of any legal proceedings but we are confident that our process for decision-making is robust and will strongly defend any challenge.”
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