British High Commissioner to New Zealand Laura Clarke says three's too much at stake for Brexit to fail.

It's been two years since the UK voted to leave the EU, and the occasion was marked with a 100,000-strong march in the streets of London against Brexit.

Meanwhile, work was going on behind the scenes, as the implementation period drew closer, and New Zealand began trade dialogues with both the UK and the European Union, to work towards free trade agreements.

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The remain voters were out in force in London protesting Brexit on the two year anniversary of the referendum.

On Monday, Clarke said while there was a lot of political noise and debate around Brexit, the UK had taken steps towards Brexiting.

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It's been two years since the UK voted to leave the EU, and British High Commissioner Laura Clarke says progress is being made. From March next year, the UK will be able to begin trade negotiations.

"It's bumpy and it's noisy, but I think that's inevitable, because we have a huge amount that we need to negotiate, we have a huge amount we need to work through," she said.

"But I think it's really important to say we are actually making progress - we are making gradual, steady progress."

In December, the UK and EU sealed a deal, which addressed citizens' rights, Northern Ireland and the financial settlement.

Tens of thousands of anti-Brexit protesters call for new vote two years after Brexit.

In March, the parties agreed on a year-long implementation period to provide continuity to business while allowing the UK to begin trade agreement negotiations.

And on July 9, the UK would publish a white paper, which would set out more detailed hopes and plans for future economic and security partnerships.

New Zealand would give priority to an EU FTA. While New Zealand had begun a trade dialogue with the UK, it would not be able to negotiate until the transition period began in March next year.

Meanwhile, formal FTA negotiations between New Zealand and the EU were launched last week, during a visit from EU Trade Commissioner Cecilia Malmstrom. The first round of formal talks would kick off next month.

"There's a huge amount more to do - it gets a bit bumpy, politically, in the UK -  there's quite a lot of debate, obviously, but we're working through it," Clarke said.

"But the fundamental thing I come back to, is there's too much at stake for us to not make this work. And there's enormous commitment and competence on both sides, to making it work."

The UK was still a European nation, which faced all the same threats as its EU neighbours, she said.

The high commissioner has been public about her decision to vote to remain in the EU, but was now committed to making the most of Brexit.

When talking about the UK's decision to leave the EU, Clarke said she often referred to the history of the union.

Many continental European countries joined the EU as they transitioned out of totalitarianism or conflict, towards democracy.

"For them, the EU is part of a real identity thing. For the UK it wasn't our journey into democratisation, it was a much more economic and rational decision, and less of an identity thing for lots of Brits.

"And so I say that by way of explaining, because it was less of an identity thing for the UK, the sovereignty sacrifice that comes as being part of the EU, sat less well."

Clarke pointed to countries not having control of their trade policy, or having the final court of appeal in their own country, as some of the sovereignty sacrifices, which came as being part of the EU.

"Because for many in the UK it didn't feel like the EU was part of their identity, there wasn't the same willingness to give [some of their sovereignty] up.

"I'm not saying that's the answer as to why the vote went as it did, but that is definitely a part of that, and it's definitely useful context."

Clarke said her priority, after six months in the job, continued to be building and strengthening the bilateral relationship between New Zealand and the UK.

"It's a relationship that's really built so much on shared history, and our people-to-people links and our sports exchanges, and the OE, and the same language, and the same humour, and all that sort of thing.

"That's a brilliant foundation, but my feeling is that we have to keep making the case anew for the relationship, because we can't take it for granted - particularly as the demographics in New Zealand are changing.

"More and more people trace their roots to other parts of the world, and they don't have grandparents who came from the UK.

"So we we need to keep making a case for the relationship, looking to the future, based on shared values, a shared vision of the future, but also a sense of where we can work together to deliver benefits for both our countries."

On of the main priority areas was boosting two-way trade, and paving the way for a post-Brexit free trade agreement, she said.

 - Stuff