UK Foreign Secretary Boris Johnson says New Zealand is a great exporter of human capital to the UK and he wants to ensure New Zealanders can "come and go" freely.
Mr Johnson is in New Zealand for a two-day visit and meets Prime Minister Bill English today.
He has suggested Britain could look at introducing some sort of special visa for Commonwealth countries once the process of leaving the EU was complete.
And, despite recent "bureaucratic foul-ups" on visas, the UK wanted to make things as smooth, generous and attractive as possible for New Zealanders.
"I am determined to ensure that New Zealanders are able to come and go with a free and cheerful va-et-vient, if I can use a Continental expression," he told Morning Report's Guyon Espiner.
As the former mayor of London, he was aware the city benefited from having dynamic versatile people come in from around the world.
"New Zealand is one of the great exporters of human capital and we massively value it. Obviously we're going to be looking at doing a deal that is going to make sure that we are going to be able to maintain and maximise those advantages."
But there would be no details until the UK had extricated itself from "the toils of the EU system".
Current arrangements, such as the youth mobility scheme and ancestry visa provisions were not too bad, he said.
Clint Heine, director of support network Kiwis in London, earlier told Morning Report the visa delays, which started when processing was moved from Manila, in Philippines, to Sheffield, had caused frustration for New Zealanders.
People who had paid extra money for urgent visas, supposed to take 10 days to process, found they were waiting 30-40 days.
Some visas were taking seven to eight weeks.
"The Sheffield processing [office] couldn't keep up with the demand, unfortunately"
People who were going to the UK on the two-year working holiday visa, and expecting an 8-10 day turnaround, were having to cancel flights and re-arrange their jobs.
He backed Mr Johnson's idea of a visa for citizens of Commonwealth countries when Britain leaves the European Union.
NZ, UK 'share outlook' on trade
Mr Johnson has said the UK wants to work with New Zealand on trade once the process of leaving the EU is complete and was "at or near the very front of the queue" for a free trade deal.
He would not be drawn on whether terms would be more favourable than at present.
"What we want is a deal that works for everybody.
"Global free trade has not been increasing in the way that it should be ... trade as a share of global growth has been falling.
"We need to stimulate it.
"The UK and New Zealand share a outlook on this. we want to work together."
Brexit was all about Britain being able to be more open and engaged with the rest of the world than before, he said.
In comparison New Zealand had been free to set its own path. If it had somehow been part of Britain's accession to the EU, it would not have been able to get rid of agricultural subsidies, and its wine industry might not have taken off.
"Would that have been possible under the EU wine regime? Might there not have been pressure for New Zealand to boil up its fantastic production of wine and turn it into bioethanol?"