In what amounted to an ultimatum, he added: 'It is important to tell the truth. The EU this week conducted more talks with Britain on a transition period after Brexit, in which London will have access to the EU's single market if it follows all the bloc's laws without having any decision-making powers.
Barnier added that he "wasn't talking about a threat" but "if this disagreement were to persist there would undoubtedly be a problem, I hope we would be able to resolve those disagreements in the next round" of talks.
Meanwhile, Tokyo's ambassador to Britain warned that Japanese businesses might pull out of Britain if they faced higher costs after Brexit.
"The UK insisted that we should reach an agreement in March on transitional period".
In December, Number 10 said it would prevent a hard border either in an overall deal, a special deal for Northern Ireland or by continuing to follow some European Union rules.
In its first public statement since the furore broke, the Open Society Foundations (OSF) warned that "human rights protections, hard-won civil and labour rights, safeguards on key issues such as clean air or food standards are at stake here for British citizens".
Mr Barnier yesterday outlined the three options for ensuring no obstructive physical borders on the island of Ireland, as per the wording of the December agreement.
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In Britain's 2016 referendum, 51.9%, or 17.4-million people, voted to leave the European Union while 48.1%, or 16.1-million people, voted to stay. The final bill will reportedly total around £50 billion (€67 billion).
Companies are heaping pressure on the British government to explain its plan for Brexit.
He confirmed the Guardian's report that, under the draft withdrawal agreement, Northern Ireland would in effect stay in the single market and customs union where relevant to the north-south economy and Good Friday agreement.
But May is not keen on freedom of movement remaining during a transition period.
But according to EU Brexit co-ordinator Guy Verhofstadt the issue of EU citizens' rights during a transition period is simply non-negotiable as the bloc will not accept a two tier situation for EU citizens.
They say they may have to move some of their units out of the country if the post-Brexit environment remains uncertain.
United Kingdom officials disputed that and said May's Brexit advisor Olly Robbins will discuss dates and agenda with the EU's deputy chief negotiator Sabine Weyand on Friday afternoon.
Transition is crucial for business as the future trade deal between the two sides nearly certainly won't have been completed on the day Britain leaves the bloc, so businesses on both sides would plunge into a legal and regulatory limbo in March next year.