Prime Minister Theresa May will visit Wales on Monday as part of a plan to engage with all the nations of the United Kingdom before she formally launches Britain's departure from the European Union.

May is due to trigger Article 50 of the EU's Lisbon Treaty, beginning two years of formal divorce talks, by the end of this month, and her office said she would be visiting Wales, Scotland and Northern Ireland to hear people's views.

Last year's Brexit referendum exposed splits that could threaten the unity of the UK, with Scotland and Northern Ireland delivering pro-EU majorities but finding themselves outvoted by the English and Welsh, who were in favour of leaving the bloc.

In a sharp challenge to May, Scottish First Minister Nicola Sturgeon said last week she would be pushing for a fresh independence vote after having been met by "a brick wall of intransigence" in London when seeking for Scotland to have its own Brexit deal. May rebuffed that, saying now was not the right time.

Northern Ireland's largest Irish nationalist party Sinn Fein has also said it wants a referendum on splitting from the United Kingdom "as soon as possible" to unite with the Republic of Ireland.

On Monday May and Brexit minister David Davis will meet with Welsh First Minister Carwyn Jones and business representatives to discuss how Wales can make the most of opportunities offered by Brexit, her office said.

"From my first day ... I made clear my determination to strengthen and sustain the precious union. I have also been clear that as we leave the European Union I will work to deliver a deal that works for the whole of the UK," May said in a statement before the visit.

"I want every part of the United Kingdom to be able to make the most of the opportunities ahead and for Welsh businesses to benefit from the freest possible trade as part of a global trading nation."