New Zealand hopes to negotiate a "high quality" free trade agreement with the UK once it leaves the EU, its prime minister Bill English has said.
Following a meeting with Theresa May, he said he hoped this would happen "as soon as possible".
Mrs May said both countries already enjoy a strong and growing trading relationship worth over £3bn last year.
International Trade Secretary Liam Fox will be visiting New Zealand in the coming months, she said.
Mrs May said her colleague would begin a bilateral dialogue between the two nations with the ultimate aim of striking a trade deal.
The small Oceanic country of less than five million people is believed to be seen in government circles as one of the best prospects for an early trade deal once Britain quits the EU.
Britain is the second largest foreign investor in New Zealand and its fifth largest bilateral trading partner.
It is also one of the global "five eyes" partners which share their security intelligence with the UK, along with the US, Canada and Australia.
Speaking at a press conference, Mr English said: "We're ready to negotiate a high quality free trade agreement with the UK when it's in a position to do so.
"We already have a strong and diversified trading relationship with the UK and a free trade agreement will build on that...
"We would hope that we could negotiate as soon as possible after the exit is completed. If the UK want to demonstrate that they can negotiate a high quality trade agreement, then New Zealand is the ideal partner for that."
Mrs May said New Zealand is important to the UK because of its historic ties, its shared values and belief in free trade.
"As two island nations we know that trade is essential to the prosperity of our countries and it's natural that we share a firm, deep-rooted belief in the power of free trade and open markets to drive economic progress and the importance of ensuring the benefits of growth are shared widely and fairly," she said.
"While the UK remains in the EU we will work together to support an EU-New Zealand trade deal and we will also look to the future and how we can expand our trade and investment partnership...
"In the longer term we agree on the potential for a bold, new UK-New Zealand free trade agreement and I look forward to starting early discussions on this in due course."