The Prime Minister says an apology from UKIP leader and Brexit advocate Nigel Farage for London turning its back on New Zealand when it joined the Common Market is unnecessary.
Mr Farage said he was sorry for the way Britain treated New Zealand producers who had enjoyed a good trading relationship before the British Government aligned with European trade blocs.
Now Brexit gave an opportunity to strengthen traditional trade ties Downunder, he said.
Mr Farage, who pressured the UK Government to hold a referendum on EU membership and was a leading figure in the Leave campaign, said: "What is even more exciting for me is what we can do with you guys. And I apologise to everybody in New Zealand for what my parents' generation did - we turned our backs on you."
He told Newstalk's Mike Hosking that it was time to negotiate good trade deals and return to how the two nations previously operated.
"We had good preferential trading terms as some of the closest friends and countries in the world. We joined the Common Market as it was then called and dealt you a very bad hand.
"Well now we can talk to you guys about having a sensible, better trading relationship and Britain once again has the chance to be a global trading nation, not just a European one."
Asked about Mr Farage's apology, John Key said the Government had no desire to "relitigate" past issues.
"Britain decided to take the steps that it took. It believed that its future was better placed in Europe, it's now decided it wants to reverse that decision in part."
Mr Farage, who came under fire during the campaign for targeting immigrants, said exiting the EU would not harm Britain as a trading nation but would improve it.
I apologise to everybody in New Zealand for what my parents' generation did.
Mr Key has already spoken to Australian Prime Minister Malcolm Turnbull about how to approach the British exit from the European Union.
"Where it makes sense, we will co-operate together," Mr Key said yesterday. "Where it is appropriate, we will do things under our own steam."
Hear Mike Hosking's interview with Nigel Farage here:
Federated Farmers president Dr William Rolleston said Mr Farage's offer to increase trade ties with Britain was welcomed. However, he viewed a looming Brexit as a double-edged sword.
"While we have got a better opportunity going into Britain, we have actually lost a free-market ally sitting around the table in Europe," he said. "The last 43 years of having Britain in the EU has opened doors for us within Europe. Those relationships - how strong they are - will be tested."
New Zealand primary exports to Britain are at 3 per cent, and 11 per cent to Europe. It was a different picture when Britain entered the European Union 43 years ago - at that time 40 per cent of exports went to Britain. And in the 1950s, more than 80 per cent of New Zealand exports went to Britain.
"There has been some commentary about a possible recession in Britain and a decrease in demand," Dr Rolleston said. "But it's not the sort of shock that we would have had, had we still been sending 80 per cent of our products to Britain. And in fact, while it was hard it has been of real benefit to New Zealand because we have come out stronger from that challenge that we had 40 years ago.
"Would we want to be in a position now where we were relying almost solely on Britain? I don't think so. The world is a better place and we are in a much stronger position. So from that point of view, he probably has nothing to apologise for."