New Zealand needs to be voicing concerns about illegal activities that occurred during the United Kingdom's Brexit vote, Prof Robert Patman says.

In the latest episode of Global Insight, the University of Otago international relations specialist says Theresa May's survival as UK Prime Minister today will do nothing to help the country out of the constitutional mess it has found itself in since voting to leave the European Union.

"The problem is Brexit itself," Prof Patman says.

"The UK will find it very hard to extricate itself after 40 years of integration with the EU."

Prof Patman says the Brexit vote was marred by "clear breaches of law" - particularly campaign expenditure and data breaches - that need to be investigated.

He calls on New Zealand and other like-minded countries to express their concerns.

"Because, if you cannot uphold the law in a liberal democracy, then everything else is at risk."