Britain would be unlikely to open its doors further to New Zealanders if it leaves the European Union, Prime Minister John Key says.
The referendum in which UK voters will decide whether to stay with the EU is on Thursday.
After taking a surprise lead in polls a week ago enthusiasm for the "leave" vote has slipped in latest polling.
But there is still little between the Brexit (pro-leave British exit) camp and those who want to remain in the EU.
When he met British Prime Minister David Cameron in Washington in April, Mr Key expressed disappointment about new restrictions around Tier 2 Visas, the skilled migrant category.
At the time Mr Key told the Herald that he recognised Britain's big issue was that there was a large amount of immigration from Europe that it couldn't control, but New Zealanders had always pulled their weight and, "why should we be penalised for the migration policies of being part of Europe?".
Asked today if a "leave" vote could lead to restrictions on migration from New Zealand being eased, Mr Key said he didn't think so.
"In so much as part of the driving motivation of the leave camp is about migration, it is hard to see them then, if they do leave, all of a sudden having a very welcoming policy on migration. So I'm a bit suspect about those arguments.
"I don't think [access] would be greatly enhanced."
Mr Key, who has said he would prefer it if the UK stayed in the EU, said New Zealand officials were reviewing what could happen in the event the Brexit camp wins.
"There is a two-year period if they do vote to leave where they are still part of the union...so we'd have a couple of years to work on that.
"Superficially it would affect things like, for instance, the free trade agreement we are negotiating with the EU, we would obviously work on the migration issues and how those rules might work."
Last week Foreign Minister Murray McCully said New Zealand has worked on shoring up its relations with other European countries which will limit any ramifications for New Zealand if the United Kingdom votes leave.
Mr McCully said the impact of a Brexit result on New Zealand would be "changes in degree only".
"If the UK were to leave the EU, it would mean an increasing reliance by us on other relationships in Europe that we have regarded as increasingly important anyway.
"It obviously is easier if the UK is in, because we've got a large traditional friend that remains a member.
"But we've been working on the assumption for quite some time that we can't be complacent about the European relationship."
Labour leader Andrew Little has said that while it was up to the people of the United Kingdom, his personal view was that it should remain within the EU.
The UK was one of New Zealand's biggest allies in the EU and Mr Little said that would be lost if Brexit won.