Prime Minister John Key says New Zealand will have to work harder to push its credentials in Europe now that the UK will no longer be a strong voice at the EU table on its behalf.

And he's cautioned that Brexit will not necessarily lead to an easing of UK migration restrictions on New Zealanders living and working in the UK given that uncontrolled migration was a key driver of the British referendum vote to leave the EU.

Speaking in London on Monday Mr Key said that this week he will touch base with UK and European government and business leaders amid the turmoil surrounding Brexit.

"The main thing will be to have an opportunity to get a bit of a sense of what they think a post-Brexit environment will look like, what they see the challenges are and obviously at some point quietly register New Zealand's interests," he told reporters.


Mr Key will meet outgoing British Prime Minister David Cameron later on Monday before later in the week meeting Italian Prime Minister Matteo Renzi in Rome and French President Francois Hollande and Prime Minister Manuel Valls in Paris.

"On the one hand I'm very confident about our position, we've had assurances both from the EU and British officials that existing access to this market will be maintained," Mr Key said.

"But longer term there are some parts of the export access that we have that we're very much looking to maintain or grow, particularly around things like lamb meat."

The prime minister said the UK had been a friend of New Zealand at the EU table, among other things advocating for New Zealand's entry into an EU free trade agreement.

"Those days are really over, they're no longer going to have a seat at the table ... Britain is no longer a voice to advocate for us, we need to do that on our own and for ourselves."

Mr Key said New Zealand had recommended the UK stay in the EU but there was no point in lamenting the Brexit decision.

"It does mean we have to put a bit more effort into pushing our European credentials.

"The challenge will be the likes of French farmers who are cautious about New Zealand, a little bit with Irish farmers as well as very large producers."

Mr Key cautioned about expecting a more open-door policy from the UK for New Zealanders wanting to live and work in Britain given that a key driver of the Brexit vote was a desire to curb migration, and an incoming British prime minister would be alert to that.

"New Zealanders have always enjoyed the rights to come and work here for a couple of years and we will want to maintain that and potentially ultimately open up the opportunities for more over time."

Mr Key said to achieve that New Zealand needed to stress its historical and family ties with Britain as well as the valuable work skills New Zealanders took to the UK.