New Zealand and Britain signed agreements on Monday to ensure trade continues to flow freely between the two countries even after Brexit.

"These agreements mean current trade-facilitating arrangements covering the export of products into the EU are maintained with the UK," Prime Minister Jacinda Ardern said in a statement after a meeting with Prime Minister Theresa May in London.

New Zealand exporters would not be worse off in the immediate aftermath of Brexit and there would be a continuity of the existing rules, she said.

In the longer term, Ardern also reaffirmed the commitment of both countries to launch negotiations on a free trade agreement once Britain has exited the European Union.

May suffered a crushing defeat in parliament in last week's vote on her Brexit deal with the EU, as the clock ticks down to March 29, the date Britain is due to leave the bloc. There is growing anxiety Britain could crash out with no deal in place.

In an interview with the BBC Ardern said a no-deal scenario for Britain would would be "very, very difficult" and "impact on just about everybody ... in particular, small business."

For the year ended June 2018, New Zealand's total exports to Britain were worth 2.95 billion New Zealand dollars (1.99 billion dollars), and the country's total imports from Britain were worth 2.7 billion New Zealand dollars.

New Zealand's agreement follows a similar deal signed with Australia last week, and is one of more than 30 planned by Britain.

Ardern next heads to attend the World Economic Forum in Davos, Switzerland, and to push to push New Zealand's case for a free trade agreement with the European Union.