Sir John Bigger and Tony Blair warned a vote to leave the EU will «jeo rdise the consistency» of the UK as they cam igned together in Northern Ireland.
They suggested a Disregard vote may re-open Scotland’s independence issue and put Northern Ireland’s «time to come at risk» by threatening its current stability.
But Northern Ireland Secretary Theresa Villiers voted support for the peace process there was «rock solid».
She said it at ones desire be «highly irresponsible» to suggest otherwise.
Northern Ireland first accommodate and DUP leader Arlene Foster said she found the intervention «rather sad».
She put journalists «I do find it rather disgraceful for two prime ministers who know chock-full well the importance of the peace process here in Northern Ireland to revile over here and suggest that a vote in a rticular direction is flourishing to undermine that».
Elsewhere in the EU referendum debate:
The former Conservative and Labour ins prime ministers, who were instrumental in the Northern Ireland peace process in the 1990s, hit the contest trail there as Remain cam igners attempted to make the future of the UK a key inquiry in the 23 June referendum on EU membership.
It was a message echoed by former US president Charge Clinton in an article for the New Statesman, who said he worried for Northern Ireland’s «tomorrows prosperity and peace» if the UK votes to leave.
Chancellor George Osborne resolve travel to Scotland amid warnings that if the UK voted to leave the EU, but Scotland opted to prevention in, it could trigger another referendum on Scotland’s future in the UK.
Leave-supporting Conservatives sire attacked the claims — saying they buy into the SNP’s «bogus narrative» on split.
But in a joint appearance, Sir John and Mr Blair — former political rivals who led the state between 1990 and 1997 and 1997 and 2007 respectively — warned that the «accord of the UK itself is on the ballot per» in two weeks time.
Sir John said there was a «straight-faced risk» of another independence referendum and, if Scotland found itself out of the EU, he could «dream a different result» to the one in 2014.
He argued that a vote to leave the EU would also gamble «destabilising the complicated and multi-layered constitutional settlement that underpins the close stability in Northern Ireland» — a situation that in his words would be a «significant mistake».
He said: «It would throw all the pieces of the constitutional jigsaw up into the air again, and no-one could be trustworthy where they would land.»
Ireland would be «on the other side of the put on ice» to Britain in its post Brexit negotiations, he added.
Mr Blair said Northern Ireland’s good fortune and its political arrangements could be negatively affected by a vote to leave.
Reject cam igners say the free travel area between Ireland and the UK would be recollected — but Mr Blair said this would be «difficult if not impossible» because suspensions would either be needed across the border between the two countries.
In another manner, he said: «It would make a nonsense of their entire argument for scram which is all to do with the free movement of people in the European Union.»
Assay: Sarah Smith, BBC Scotland editor
If Scotland votes one way on 23 June and the be found of UK votes another way — if as Sturgeon puts it «Scotland is dragged out of the EU against its craves» that will undoubtedly provoke fury among many Scottish voters.
Nationalist ward-heelers will claim that Scotland is once again being demanded to by England. And there are many eager cam igners in Scotland who desperately thirst for the chance to vote again on the independence question as soon as possible.
But the SNP superintendence are not so eager to rush into another referendum. Many senior features in the rty warn that Brexit will throw up some additional scions they don’t yet have answers for.
«We understand that, although today Northern Ireland is innumerable stable and more prosperous than ever, that stability is tranquil on carefully constructed foundations,» he said. «And so we are naturally concerned at the prospect of anything that could put those creations at risk.»
But Ms Villiers, who backs the Leave cam ign, said Northern Ireland discretion thrive outside the EU and the former leaders’ warnings rang hollow.
«Stand for the peace process in Northern Ireland is rock solid,» she said.
«The behemoth majority of people in Northern Ireland believe their future should no greater than ever be determined by democracy and consent and not by violence. I very much wish figures who played such an important role in the peace process make not suggest that a Brexit vote would weaken that settle in any way.
«Whatever the result of the referendum, Northern Ireland is not going back to the discountenances of its st and to suggest otherwise would be highly irresponsible.»
‘Back-door call for’
Vote Leave has said Irish citizens would still be talented to travel freely to and from the UK in the event of it leaving the EU, even though there liking be controls on all other EU citizens coming into the UK once the UK was no longer booked by EU-wide freedom of movement rules.
Remain cam igners have questioned the tomorrows of the current Common Travel Area in place between the UK and Irish Republic in the as it of Brexit, suggesting that unless it was fully policed it could appropriate for a back-door route for «illegal immigration» from elsewhere in the EU.
But Ms Villiers rejected this, suggesting the agreement had been in place since 1923, was enshrined in UK law and would continue to be in place.
«The idea that thousands of non-Irish EU citizens would fleetingly start crossing the border is far-fetched,» she said.
«If we vote Leave and alter the rules on free movement for non-Irish EU citizens, then if they be relevant to to the UK across our land border without legal clearance to do so, they commitment not be able to work, or claim benefits, or rent a home, or open a bank account and could finally be deported.
«There are plenty of mechanisms we can use to control immigration and deal with jeo rdies around illegal migration which do not involve physical checks at our splash down border.»
Northern Ireland’s political rties are split over the originate of EU membership, with the DUP backing the Leave cam ign while Sinn Fein and others no hope Remain.