Prime Minister Jacinda Ardern says she is confident New Zealand will still be one of the "first cabs off the rank" for a post-Brexit free trade agreement with the United Kingdom.

Ardern met with British Prime Minister Theresa May on the garden terrace at 10 Downing Street on an unseasonably warm London day, walking in soon after Canada's Prime Minister Justin Trudeau walked out of his meeting.

Both spent half an hour with May before they met again for the intelligence meeting of the four Five Eyes leaders in London for the Commonwealth Heads of Government meeting.

May committed to putting New Zealand at the top of the list for post-Brexit trade agreements last January when former Prime Minister Bill English visited her at Downing St.

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Since then the change of government in New Zealand has seen a shift in the focus of trade agreements - while National focused heavily on the economic promise of trade agreements, Ardern's Government wants to ensure they also cover environmental and social factors such as labour.

Australia and the United States have been added to make the top three for the UK, although recent moves by the US to impose tariffs could make that agreement more complex.

Trudeau's presence was a reminder other countries are happy to take New Zealand's place. Canada is looking at other trade agreements lest the Nafta agreement is affected by US President Donald Trump.

Ardern said she believed New Zealand was still well placed to be one of the first to sign with the UK because of its size and experience in trade agreements.

The UK wants to get some easy and strong trade agreements under its belt quickly to prove it can survive outside the EU and to set a standard for other, trickier agreements that might follow.

May has also been canvassing leaders about how to respond to a range of issues including the nerve agent poisoning of former Russian spy Sergei Skripal in the UK, the use of chemical weapons in Syria and cyber attacks for which May and some other countries are blaming Russia.

Ardern said May had already thanked her publicly and in private over New Zealand's stance on the nerve gas.

Before the meeting began, May was asked about New Zealand's response and answered by saying the two countries had "very good" relations and she was pleased with the international support for Britain over the nerve gas issue, without specific reference to New Zealand.

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New Zealand was slower than other countries such as Canada and Australia to unequivocally say the evidence pointed to Russia being behind the nerve gas poisoning, and did not follow other countries' leads in expelling diplomats, because Ardern said there were no undeclared intelligence agents acting as regular diplomats in New Zealand.

Ardern said May did not raise that with her.

The conversation with May was part of a hectic day for Ardern in London. She first met up with London Mayor Sadiq Khan at City Hall, followed by a joint meeting with about 60 secondary school students. Then came a chat with Prince Charles and Camilla at Clarence House before the meeting with May. Next, the four leaders of Five Eyes countries in the UK met up: Ardern, May, Trudeau and Australia's Malcolm Turnbull.

The day ended with a reception hosted by May for the 51 Commonwealth Heads of Government in London. The serious talks in the CHOGM summit begin tonight - and Ardern will also meet with the Queen for the first time.