United Kingdom seeks to remain member of some European Union agencies

Media playback is unsupported on your device                  Media caption Donald Tusk said his transport was'not frictionless

Also speaking to the BBC on Sunday, the Prime Minister said her overall Brexit plan for Britain to align with European Union rules to allow for "frictionless" trade while retaining the leeway to diverge from them was "ambitious" and "credible".

The PM accepted the UK's "responsibility" to help keep a soft border with the Republic - setting out in detail how she believed this could be achieved through technological means or a broader trade deal.

"This is the mistake that is made in Britain all the time", he said.

Mr Coveney said if agreement can not be reached during tripartite talks between the UK, Ireland and the EU Commission, the backstop plan of full British alignment with customs union and single market rules that Mrs May "committed clearly" to in December's conclusion of withdrawal negotiations would have to be put in place.

May's speech did offer some proposals to solve some of the thorniest problems thrown up by Brexit, especially over Ireland, after the EU set out in a draft withdrawal agreement a backup plan that effectively would see Northern Ireland remain part of the EU's customs union.

The deputy prime minister, Simon Coveney, welcomed the UK's reiteration of its commitment to the Good Friday agreement, but said that "these commitments now need to be translated into concrete proposals on how a hard border can be avoided".

The Health Secretary said there would be a "pragmatic alignment of regulations" with the Brussels to ensure access to European markets, but that MPs would get control of the power to choose to diverge from EU rules, with knowledge of the consequences.

But Downing Street and Boris Johnson have denied reports that Mrs May's chief of staff Gavin Barwell was behind a leak of the Foreign Secretary's private thoughts on the contentious issue of the Irish border, which is holding up Brexit negotiations.

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McDonnell has said today that the United Kingdom should not prioritise one concern over the other. Big business echoed his words and even some Brexit campaigners praised the prime minister for her pragmatism.

May says Brexit talks are approaching a crucial moment and "there is no escaping the complexity of the task ahead of us".

She defended her position by saying Britain could not become a "rule taker" when it came to financial services. "We will not be buffeted by the demands to talk tough or threaten a walk-out", she said.

"I remain concerned that some of the constraints of leaving the customs union and the single market are still not fully recognised", the taoiseach said.

But Dublin and Brussels remain to be convinced that this can be avoided after the United Kingdom leaves the EU's customs union, unless Northern Ireland continues to abides by its rules and those of the single market.

Scottish First Minister Nicola Sturgeon, an opponent of Brexit, said May could no longer get away with "vacuous, meaningless rhetoric".

May, 61, has long kept her cards close to her chest, trying to avoid provoking those in Britain who want a clean break with the European Union, or others who fear the world's sixth-largest economy will suffer if barriers are raised against a major trading partner.

But he insisted that for a single market to function "if goods move from one customs union to another there needs to be some checks" unless some mechanism was negotiated to prevent them.

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