The Irish PM has ramped up the rhetoric by threatening to block planes from flying over his country to the UK if the EU's demands are not met.

Leo Varadkar said Britain could not expect to 'use other people's sky' after leaving the bloc if there is no deal on future relations.

But the sabre-ratting was derided by critics who pointed out that airspace rules are governed by an entirely separate international treaty - and most flights to Europe go over British airspace.

Hugh Bennett, a Brexit campaigner, posted an image showing the vast majority of Irish flights heading over the UK.

Writing on Twitter, he added: '[The] Taoiseach says he won't let UK planes fly over Ireland in the event of a "hard Brexit".

'Hope he likes going on holiday to Lanzarotte because he's going to have trouble flying anywhere else.'

He also pointed out that a key part of the airspace to the west of Ireland is controlled by the UK - again proving his threat toothless.

The row comes as Theresa May is visiting the Irish border today for talks with local businesses and residents as she seeks to shift the biggest obstacle to a deal with Brussels.

Irish PM Leo Varakdar (pictured) has ramped up the rhetoric by issuing an extraordinary threat to block planes from flying over his country to the UK if the EU's demands are not met

Theresa May (pictured today in Northern Ireland with DUP leader Arlene Foster) is facing a battle on all fronts to get her Chequers Brexit blueprint through

The Prime Minister (pictured during a visit to a pottery factory in Northern Ireland with DUP leader Arlene Foster) has insisted that she will get a good deal for the UK - but Brexiteers and Remainers have both lashed her proposals

A Twitter user was quick to point out that the vast majority of planes leaving Ireland fly over the UK - meaning that if the two countries blocked each other's plans, Leo Varadkar would have very little choice about where he went on holiday

Hugh Bennett, a Brexit campaigner, also pointed out that the UK controls a key part o the airspace near Ireland - again scuppering the Irish PM's threat

The jibe from Mr Varadkar underlines the increasingly entrenched position being adopted by Brussels in the negotiations.

The EU has demanded Britain chooses between two options for avoiding a hard Irish border - an outcome both sides say they do not want.

The first option would see a 'Norway plus' arrangement with the UK remaining in the single market and customs union - accepting free movement and obeying Brussels rules without having any say in setting them.

The other option is a limited Canada-style free trade agreement for the British mainland - but Northern Ireland would effectively remain a part of the EU.

Mrs May has said both blueprints are totally unacceptable, and put forward a compromise plan that would see the UK follow rules on goods and collect some tariffs on behalf of Brussels to avoid border friction.

Eurocrats regard the ideas as 'cherry picking'.

Mrs May will meet business representatives on the Northern Ireland side of the border this afternoon.

Tomorrow she is due to deliver a speech in Belfast focusing on how her vision of Brexit, outlined in last week's Government white paper, will impact Northern Ireland and the border.

But Mr Varadkar upped the ante last night by telling journalists 'planes will not fly' if Mrs May did not convince the EU there will be no hard border.

New Brexit Secretary Dominic Raab (right) is facing off with the EU's Michel Barnier (left) for the first time in Brussels today

'The situation at the moment is that the United Kingdom is part of the single European sky, and if they leave the EU they are not and that does mean that if there was a no deal hard Brexit next March the planes would not fly and Britain would be an island in many ways, and that is something that they need to think about.

'You can not have your cake and eat it. You can't take back your waters and then expect to use other people's sky.'

He added: 'In the unlikely event that we have a hard Brexit next March, with no deal, I think every country will struggle to put in place the necessary infrastructure and customs and veterinary officials in their ports and airports. It won't be just us.'

Ahead of her arrival, Mrs May said: 'I look forward to hearing views from businesses on the border in Northern Ireland on our departure from the European Union.

'I fully recognise how their livelihoods, families and friends rely on the ability to move freely across the border to trade, live and work on a daily basis.

'That's why we have ruled out any kind of hard border. Daily journeys will continue to be seamless and there will be no checks or infrastructure at the border to get in the way of this.

'I've also been clear we will not accept the imposition of any border down the Irish Sea and we will preserve the integrity of the UK's internal market and Northern Ireland's place within it.'

Mrs May will also hold talks with the region's political parties on the two-day trip, with separate bilateral meetings scheduled across both days.

Northern Ireland has been without a properly functioning devolved government for 18 months due to a bitter fallout between the two biggest parties - Sinn Fein and the Conservatives' confidence and supply partners at Westminster, the Democratic Unionists.