New Zealand and Britain have signed an agreement which gives certainty to New Zealand businesses if Britain leaves the EU from the European Union with no plan in place.

Prime Minister Jacinda Ardern met her British counterpart Theresa May at 10 Downing St early today (NZT) to reiterate New Zealand's interest in pursuing a free trade agreement following Brexit.

Ardern told reporters after the meeting that a mutual recognition agreement had been signed by New Zealand High Commissioner to the UK Sir Jerry Mateparae and British Trade Secretary Liam Fox.

It is similar to one Australia has already signed with Britain and rolls over to the UK the trading framework New Zealander businesses have with the EU post-Brexit on March 29.

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"Essentially what that will mean for New Zealand business is that they will be no worse off, regardless of scenario, from the day any Brexit arrangements come into force," Ardern said.

"It means that our businesses can continue with confidence, knowing that our products will continue to be treated in the same way in the UK here that they are by, for instance, the EU.

"It gives that certainty that I think our businesses and our exporters, particularly our meat producers, will be looking for."

Ardern called the agreement an interim undertaking but said it was "incredibly important from our perspective that the moment we see the final response on Brexit that we are able to see our businesses continue to operate here in the UK in the way they currently are able to".

Ardern described her meeting with May as constructive. Although she and May had discussed a future free trade agreement, she stressed that negotiations couldn't begin until Britain had concluded its Brexit negotiations.

They met just before May went back to the House of Commons to tell MPs how she intended to proceed after her original Brexit deal was soundly rejected last week.

May said she would consult other political parties on changes to her deal before going back to Brussels to seek new concessions, particularly around the prospect of a hard border between Northern Ireland and the Republic, but did not rule out a no-deal Brexit deal on March 29. She did, however, again rule out the prospect of a second referendum.

Speaking in Parliament, May addressed jeering when she told MPs she had discussed a future trade deal with Ardern by also saying they had also talked about the possibility that the United Kingdom may join the Comprehensive and Progressive Trans-Pacific Partnership.

"Before Members opposite start talking about the size of New Zealand, not just a trade deal with New Zealand but actually, membership of the United Kingdom in the CPTPP," May said.

The CPTPP's 11 signatory countries, which include New Zealand, agreed at the weekend to guidelines for joining, saying the trade pact was open to all economies which accepted its principles.

Ardern welcomed the UK's interest in joining.

"New Zealand supports the expansion of CPTPP to parties willing and able to meet the high standards of the agreement," she said.

In what Ardern described as a "wide-ranging discussion", she and May also discussed immigration issues for New Zealanders in the UK.

"New Zealanders continue to contribute to the UK economy and we welcome large numbers of UK citizens to New Zealand, including on our popular working holiday scheme. I welcomed the recent announcement that New Zealand citizens will soon be able to use e-gates in the UK," Ardern said.

Prior to her meeting with May, Ardern visited Lloyd's of London for a Brexit discussion that included business leaders and London Mayor Sadiq Khan.

"Real enthusiasm in that room for a future free trade agreement with New Zealand, and I think you hear the business community here in the UK talking with such enthusiasm and that really makes me optimistic about our future opportunities here," she said.

Ardern travels to Switzerland next for the World Economic Forum where she and Finance Minister Grant Robertson will be showcasing New Zealand's wellbeing budget, which she described as a "world-first".

Ardern also takes part in three panel discussions and will hold a number of sideline meetings with other world leaders.

She then travels to Brussels to push New Zealand's case for a free trade agreement with the European Union.