John Key says he doesn't know Britain's soon-to-be prime minister Theresa May very well but his impression is she's a straight shooter and others speak highly of her.

The prime minister is in London where Ms May has just been announced as the next Conservative Party leader and incoming prime minister after her only rival, Andrea Leadsom, quit the contest.

Ms May, 59, is Home Secretary and will take over from David Cameron on Wednesday.

Mr Cameron announced his resignation after the Brexit vote, and Mr Key on Monday became one of the last visiting leaders to meet him at No. 10 Downing Street.

John Key became one of the last visiting leaders to meet David Cameron in London. Photo / Getty Images
John Key became one of the last visiting leaders to meet David Cameron in London. Photo / Getty Images

"It was quite a dramatic day for him," Mr Key told reporters at New Zealand House after the meeting.

He said Mr Cameron was "reasonably reflective" but also "quite upbeat" as he started packing boxes at No. 10.

"Anyone who's been prime minister always naturally wants to stay in that job because it's a great privilege to lead your country.

"But he's very committed to make sure that the best is achieved for Britain over the next few years.

Mr Key said Mr Cameron was "extremely grateful" for the support New Zealand had given him and the personal friendship the two prime ministers had formed in that time.

He said he had met Ms May most recently when they discussed the migration and visa rights of New Zealanders in the UK.

"David was very effusive about her, he said she's obviously extremely intelligent, hard working, very much a straight shooter, what you see is what you get.

David Cameron has been caught appearing to sing a little tune as he re-entered Number 10 after announcing Theresa May would be Prime Minister by Wednesday evening (Thursday NZ time).

"That was certainly my impression at the last meeting I had with her," Mr Key said.

"I've no doubt over time we'll be able to build a strong relationship."

Mr Key said he had spent Monday talking to British business leaders, politicians and the governor of the Bank of England, as well as Mr Cameron, about Brexit and its implications.

"The one clear thing that's come through all the discussions we've had today ... is that they're very uncertain about what a post-Brexit environment looks like."

Mr Key said the UK would need to get back to doing trade deals when it was out of the EU and in his meetings on Monday, New Zealand's expertise in trade negotiations had been raised.

"So it's not just All Black they're after, I think it's trade negotiators as well."

Mr Key said preserving the access New Zealand had into the UK for exports such as lamb was important and his government looked to expand on that.

The prime minister later this week meets with Italian Prime Minister Matteo Renzi in Rome and French President Francois Hollande and Prime Minister Manuel Valls in Paris, with Brexit high on the agenda.