Before Thursday's referendum, in which UK voters will decide whether to stay in the EU, Mr Peters attacked Prime Minister John Key for supporting a "remain" decision.
"'Leave' is our best chance to reverse the steady loss of access rights Kiwis have in the UK," Mr Peters said.
"'Leave' is our best bet to make the Commonwealth and the institutions we share strong and enduring."
In a dig at outgoing High Commissioner to Britain Sir Lockwood Smith, Mr Peters said a leave vote would make that position pivotal, "not a scenario that Mr Key seems remotely prepared for".
British Prime Minister David Cameron, who wants Britain to remain in the EU, has "recruited all his mates", Mr Peters said.
"Aside from Messrs Key and Obama, they include India's Prime Minister Narendra Modi, Canadian Premier Justin Trudeau, and whoever Australia's prime minister of the week is.
"Anyone who thinks Britain cannot stand on her own two feet should seriously re-read their history," said Mr Peters, who last month delivered a pro-Brexit speech at the House of Lords, after an invitation by UK Independence Party (Ukip) peer Lord Pearson of Rannoch.
"Many Britons will ask themselves how Winston Churchill would have responded to fearmongering prime ministers like Mr Key, and they'll vote accordingly."
After taking a surprise lead in polls a week ago enthusiasm for the "leave" vote has slipped in latest polling. Mr Peters attributed the change in polling to the murder of British Labour MP Jo Cox.
There is still little between the Brexit 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 for skilled migrants.
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 yesterday 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 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 ramifications for New Zealand if the United Kingdom votes leave.
Mr McCully said the effect of a Brexit result on New Zealand would be "changes in degree only".
"It would mean an increasing reliance on other relationships in Europe that we have regarded as increasingly important anyway."
Labour leader Andrew Little has said that although 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.
