Before applying, would-be applicants can register on the site to check if their skills are in demand, explore visa options and check if they meet immigration criteria.
Massey University sociologist Professor Paul Spoonley said he was not surprised by the spike.
"I anticipate that post Brexit and if [presidential candidate Donald] Trump wins in America, you're going to see a spike in interest from people there about coming to New Zealand.
"We saw it during the Bush years from Americans, and I think over the next three to five years, you're going to see a significant increase in the numbers of migrants coming from both Britain and the USA."
Spoonley said middle-class professionals wanting a different lifestyle would be attracted to New Zealand.
"Brexit is the push factor and it confirmed the exclusive or narrow nationalism of the UK, of some at least," he said.
"We'd be getting people from the UK who are tired of a narrow-minded Britain and who want to experience something quite different.
"New Zealand is very different, it is multicultural, very tolerant and it's got a good lifestyle and a more temperate climate."
Spoonley noted Britain had almost the same land size as New Zealand, but its population was 64 million compared with 4.7 million here.
"Migrants move for lifestyle reasons as much as they do for economic reasons, and New Zealand has a pretty good deal on offer."
Britain had traditionally been New Zealand's main source country for permanent migrants.
It was overtaken by China in 2014, which has remained the largest source of immigrants since.
Spoonley did not think many of the Britons who registered interest would actually migrate. He believed China and India would continue to dominate immigration numbers in the foreseeable future.
Last month, Immigration accepted 272 applications for residence by Britons and 566 Chinese applications.
"The size and the depth of the Chinese middle class, and the push factors like pollution in China, always is going to mean the Chinese are going to be a very significant source of immigrants."
New Zealand experienced its largest population growth in the 12 months to June this year as a result of international migration.
Net migration was 69,100, with 125,100 migrant arrivals less 56,000 departures. Last year, 4549 British nationals gained NZ residence, 21,999 were granted work visas and 1388 student visas.
#ratherbekiwi
What's not to love? After all:We have better weather.
• We have a rugby team that actually plays rugby.
• We're more than 18,000km from Boris Johnson.
• We have affordable houses and there's no traffic (if you move to Invercargill).
• And we have our very own distinctive flag. Oh.
UK immigration to NZ
• 998 registrations on the day of Brexit referendum
• 10,647 registrations since the vote
• 272 applications for residence last month
(source: Immigration New Zealand)
