That frustration was reinforced by EU Commission President Jean-Claude Juncker, who also told EU legislators that "there is increasing urgency to negotiate this orderly withdrawal".
"It is obvious that we need further clarity from the United Kingdom if we are to reach an understanding on our future relationship", Juncker said. "The four freedoms, including the freedom of movement, are indivisible", he told MEPs in Strasbourg as they debated their vision of the post-Brexit future.
"You can not be part of our agencies without the legal commitment to apply European Union law and the jurisdiction of the court of justice", Barnier said.
"It is time to face up to the hard facts", he added.
"It is our responsibility to detail operationally how we will avoid a hard border on the island of Ireland without another solution and bearing in mind the decision of the United Kingdom to leave the single market and the customs union", he said.
Mr Juncker was cheered by Eurosceptic MEPs as he noted the UK's departure was due on March 29th, 2019. "As my good friend [the former Irish PM] John Bruton wrote in a recent article, "The most valuable test that Mrs May wishes to apply to a Brexit agreement is that it should be one that would endure and not require constant renegotiation". We see this with Brexit, we see this with trade, we see this across the board".
"As the clock counts down, with one year to go, it is now time to translate speeches into treaties, to turn commitments into agreements".More news: Meghan Markle attends first official event with the Queen
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Barnier meanwhile said a whole range of options for third-country cooperation were on the table - the European Union has previously cited trade deals of the type it has with Canada and South Korea.
The draft, which must get Britain's consent if there is to be a Brexit deal, will make agreements on the financial settlement, citizens' rights, the Irish border and a transition period legally binding.
Responding to their applause, Juncker said the time would come "when you will regret your decision". "For us this is not an Irish issue". It is all for one, one for all. "It is all for one and one for all - that is what it means to be part of this union", he said.
The European Union's chief Brexit negotiator warned Britain Tuesday against undercutting EU rules and regulations that underpin anything from social protections to food security when it leaves the bloc.
'If you decide to jettison, leave behind, the common agreements and rules, then you have to accept that things can not remain as they are'.
The EU is determined to prevent Britain from picking particular benefits of close integration without sharing the costs and obligations, fearing such an example would tear the bloc apart with more countries trying to follow suit.