Transport secretary Chris Grayling said today "rapid progress" was being made on securing fresh arrangements with third countries such as the US and Canada.
He also stressed that it was "inconceivable" that planes will stop flying when Britain leave the European Union in 2019. "It's not going to happen," Grayling added.
Speaking at the Airport Operators Association annual conference today, Grayling said: "I think it's a big leap to believe, if you take one example, that the Spanish government will not want planes to fly from the UK to Spain in the summer of 2019."
Grayling said the economic impact for Spain "would be enormous".
He also addressed questions over whether the likes of Germany and France would seek to limit Britain's access to their markets.
"What I would say is if the French were in the business of closing down air routes between France and the UK, why did Air France and KLM spend hundreds of millions of pounds in buying a stake in Virgin Atlantic, which is predominantly a transatlantic airline running out of Heathrow?" Grayling said.
The chancellor had said earlier this month it was "theoretically conceivable" planes could stop flying, but that nobody thought that would actually occur.
Airline and aviation bosses also told MPs on the Transport Select Committee today that they were confident planes will continue fly, regardless of the outcome of Brexit negotiations.
British Airways owner IAG's chief executive Willie Walsh said:
The prospect of there being no flying between the UK and Europe, I don’t agree with at all, because it goes well beyond that. I think this would bring the whole of Europe to a standstill. It’s not just about isolating the UK.
Meanwhile, the transport secretary said that as well as seeking "a positive open skies agreement with the European Union", progress was being made on talks with third countries.
At present, services to places, such as Canada and the US, are determined by EU-negotiated arrangements.
"I am pleased to say that we are making rapid progress towards securing post-Brexit arrangements with those countries," Grayling said.
Meanwhile, Heathrow's chief executive John Holland-Kaye, said that the aviation industry should look to focus on positives around Brexit.
"I hope we’ve moved on from worrying about Brexit to looking at the opportunities that come out of Brexit, and showing how the aviation sector can play a positive part in making sure Britain is a winner as we leave the EU," he said today.
"We tend to look at the negatives in Brexit, and the anxiety around it, but actually, Brexit has highlighted just what an important role aviation plays in the UK's economy," Holland-Kaye said.
He did though, seek to emphasise the importance of lining up aviation agreements for Britain's departure from the bloc.
"We are not just another economic sector, we are the enabler for all other economic sectors," the Heathrow boss said.
"Unless special aviation arrangements are put in place, it doesn't matter having WTO [World Trade Organisation] agreements for other sectors," he added. "If you're trying to get your pharmaceuticals around the world, you just physically won't be able to get them there, unless we have the right aviation agreements."