"The UK is an important market for New Zealand high- value chilled lamb exports and Brexit falls at a critical time of our Easter trade".
May met with Ardern in London on Monday.
"Such a question is actually very surprising, and the prime minister's reaction suggested that she was entirely surprised by it", Edward said.
New Zealand Prime Minister Jacinda Ardern and British Prime Minister Theresa May signed agreements on Tuesday in London, which will assist in ensuring trade continues to flow freely between the two countries in a post-Brexit environment.
A modern, high-quality free trade agreement (FTA) between New Zealand and the United Kingdom would go a long way towards unlocking this potential, enabling businesses in both countries to work more closely together to seize opportunities in the global economy.
In a press statement Ardern said NZ welcomed the UK's interest in joining the CPTPP.
"As a very important trading partner for us, at the point the United Kingdom is ready to do so, we're very keen to enter into a free trade agreement", she told the BBC's Victoria Derbyshire programme.
"There's still different layers of action and activity and I think some of those messages that are being sent will still probably cut through Davos and who is in the room, " Ms Ardern said.
"If there's a "no deal", it's hard to know how then that might play out".
May suffered a crushing defeat in parliament in last week's vote on her Brexit deal with the European Union, as the clock ticks down to March 29, the date Britain is due to leave the bloc.
The meeting is part of Ms Ardern's trip around Europe which she will finish in Brussels, where the focus will be progressing a free trade agreement with Europe.
"He mentioned specifically his appreciation for New Zealand, his love of New Zealand's native birds, and in particular his love of the kākāpō. he also mentioned the work we'd done around reducing predators and pointed out that the knees of rats shake when New Zealand is near because of our success in tackling predators", she said.
Meanwhile, the National Party said a full trade deal was the ultimate goal.
The Duke and Duchess of Sussex meet New Zealand Prime Minister Jacinda Ardern, at Government House in Wellington, New Zealand on day thirteen of their Royal Tour in October 2018. "But what will of course be required is, over time, more than that, a substantive, full, free trade agreement", he said.
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