Voters should be offered a say on the reunification of the whole of Ireland in light of Northern Ireland's vote to remain part of the EU, according to Sinn Fein's Martin McGuinness.

Mr McGuinness said there was a "democratic imperative" for a border poll to see whether Northern Irish voters wished to unite with the Irish Republic as a result of the result in which 55.8 per cent supported Remain. "We have a situation where the north is going to be dragged out on the tails of a vote in England," he added.

"The British government now has no democratic mandate to represent the views of the North in any future negotiations with the European Union and I do believe that there is a democratic imperative for a border poll to be held.

"We are now in unchartered waters, nobody really knows what is going to happen. The implications for all of us on the island of Ireland are absolutely massive. This could have very profound implications for our economy."

However the First Minister Arlene Foster and the UK Northern Ireland secretary Theresa Villiers both immediately rejected the call, saying that the necessary conditions for such a border poll had not been met.

Under the terms of the Good Friday Agreement, a border poll can only be called by the region's Secretary of State in circumstances where there is clear evidence of a public opinion swing towards Irish unity.

The most immediate impact from the Brexit vote in Northern Ireland was an apparent surge in interest in applying for an Irish passport.

Another part of the Good Friday agreement entitles anyone born anywhere in Ireland, north or south of the border, to claim a passport from the Republic - and hence effective 'membership of the EU.

Google searches for the phrase "Irish passport" rocketed as the result became apparent, from a normal rate of around three an hour to hundreds, peaking in the early hours of Friday morning.

Possession of one would mean the owner is still able to travel freely within the European Union but also to move around to live or work.

Professor Pete Shirlow from Queen's University Belfast said: "It's very simple. if you have an Irish passport you will still be part of the European Union and you will be able to move, live in the European union."

There was also speculation that border controls may have to be reintroduced, once a UK exit from the EU is negotiated. After this, Northern Ireland will become the only country in Britain which will have a land border with the EU.

Highly symbolic at the height of the Troubles, border checks were also a practical annoyance for many people, leading to routine delays sometimes of an hour or more for those travelling between north and south.

The Remain campaign had warned that a hardening of border controls would be impossible to avoid post-Brexit.

Free travel may be difficult to preserve if the EU demands checks for security reasons or on goods for import and export duties. Likewise if new UK immigration controls such as the proposed "Australian" points-based system, the current Common Travel Area, allowing free movement between the UK and Ireland could be affected.

However Ms Foster said a hard border would not be necessary. She said: "With common sense between us, the UK and Ireland can maintain a border which is just as open after a Brexit vote as it has been for many years."

In the Republic, Taoiseach Enda Kenny said keeping Ireland's borders with Britain open is a key priority.

After briefing his cabinet on the fallout from the poll, Mr Kenny said he was very sorry to see the UK leave the European Union but said his Government had contingency plans in place to limit impact on trade, the economy, relations with Northern Ireland and the common travel area between Ireland and Britain.

Mr Kenny said: "We will approach these issues in the same spirit of partnership that has underpinned the peace process and has transformed relationships on this island since the Good Friday Agreement."

"While Ireland's future lies within the European Union, Ireland's strong and close relationship with the UK will remain."

Talks are planned for July 4 between the Taoiseach and Northern Ireland's First and Deputy First Ministers Arlene Foster and Martin McGuinness when the North/South Ministerial Council meets.

"For our part, the Irish Government will do our utmost in upcoming discussions to maintain the Common Travel Area and minimise any possible disruptions to the flow of people, goods and services between these islands," Mr Kenny said.

Much remains unclear however. Dublin born Edinburgh International Festival director Fergus Linehan said: "Everybody is very anxious about it and how it affects the delicate balance in the north. But nothing is tangible."