Confusion over air travel after Brexit has intensified with the Irish prime minister at odds with the UK transport secretary.

Ireland's taoiseach, Leo Varadkar, warned that, in the event of a disorderly exit from the European Union, British airlines could be banned from Irish airspace.

At present the UK benefits from “open skies” rules, which allow EU airlines to fly between and over any European airspace.

But the Irish leader said: “If there was a no-deal hard Brexit next March, the planes would not fly and Britain would be an island in many ways.

“If they want their planes to fly over our skies, they would need to take that into account.”

In a reference to Theresa May’s plans to restrict fishing rights in UK waters, Mr Varadkar said: “You can’t have your cake and eat it. You can’t take back your waters and then expect to take back other people’s sky”.

But Chris Grayling, the transport secretary, has insisted that aviation would be unaffected even in the event of a “no-deal” Brexit.

Speaking to The Independent at the Farnborough Air Show, Mr Grayling said: “The European Commission itself – earlier this year, when publishing its negotiating guidelines – said that in all circumstances, whether there is a Brexit deal or no Brexit deal, there has to be an aviation agreement.

“I expect that, come what may, we will have a sensible agreement on aviation, because that’s what we want and that’s what they want.”

Were Ireland to ban UK aircraft from its skies, the effect would go far beyond links to and from the Republic.

London is the main European hub for transatlantic aviation, and most flights to and from the US East Coast – including Boston, New York and Washington DC – fly over Irish airspace.

But were Britain to respond, many flights from Ireland would not easily be able to reach Continental Europe.

In addition, Ryanair could be seriously affected. Europe’s biggest low-cost airline has its largest hub at Stansted airport.

Ryanair has set up a legally separate UK operation, while easyJet has established an Austrian subsidiary to ensure it can continue to fly within the EU.

Most senior aviation figures believe an agreement to maintain the existing pattern of flying is likely.