Evans welcomed the news, saying it was a "relief" that a transitional deal had been agreed: "With annual insurance contracts coming up for renewal it was critical to provide some temporary certainty to insurance customers on issues like driving in the European Union and the EHIC".
The UK has accepted the need for a backstop to be written into the Brexit withdrawal agreement.
The latter will now go to European Union leaders meeting here on Thursday and Friday for their approval and to open the next phase of talks.
Both sides agreed to intensify talks to keep people, goods and services moving across the Irish border, even though the Europeans are still waiting to hear suggestions from Britain that would avoid a "hard border".
Work on that would proceed in the next few weeks.
The backstop, described by Minister for Foreign Affairs Simon Coveney as "our insurance policy", provides that the North will maintain regulatory alignment with the South should no other broader free trade agreement between the European Union and Britain prove possible.
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In a sign of how negotiating future trade ties with what is still one of the bloc's three biggest economies will test the unity of the 27, member states are already pushing their own interests on some issues. The accord which they had reached, he said, was "much clearer than December".
Britain is due to leave the 28-nation European Union in a little over a year, and how to keep open the all-but-invisible border between European Union member state Ireland and Northern Ireland, which is part of the United Kingdom, is proving one of the biggest headaches.
The guidelines include language underlining that access for British-registered firms will be subject to ensuring financial stability and the existing legal structures of the EU. He stressed that time was running out fast. "But we are also looking forward to more precision on the details of the end-stage of the relationship".
"It's an absolute abject betrayal of Britain's fishing industry and coastal communities", he said.
Hammond has said that a post-Brexit trade agreement that doesn't include services wouldn't be "fair and balanced".
"I believe we are all encouraged by the latest progress in the Brexit negotiations".
Scottish Conservative MPs are set to meet the prime minister about the issue on Tuesday following criticism of the decision. We are going in the right direction.