Britain exiting the European Union without trade deals in place could see tensions rise between the E.U.'s Republic of Ireland and the U.K.'s Northern Ireland, according to former Irish Prime Minister John Bruton.

"It will put the Good Friday agreement at risk," Bruton told CNBC on Thursday, referring to the 1998 agreement that implemented a free border between the Irish Republic and Northern Ireland.

Under U.K. Prime Minister Theresa May's Brexit agreement, which failed to obtain sufficient parliamentary approval this week, a clause known as the Irish backstop would have ensured an open frontier between those two territories. But since that framework is no longer on the table, customs checks will be implemented between the Irish neighbors when Britain leaves the E.U. on March 29 — unless May and British lawmakers delay that deadline or decide on an alternative withdrawal strategy.

Trade barriers between the Irish Republic and Northern Ireland "will mean psychological and political isolation," warned Bruton, who was the Irish premier from 1994 to 1997, and E.U. ambassador to the United States from 2004 to 2009.

"I think a lot of people in Britain don't understand the importance of maintaining an open border in Ireland," he said. "We've created peace on the basis that the nationalist community of Northern Ireland would not be isolated from the rest of Ireland by there being an open border, and that the unionist community would not be isolated from Britain by there being free exchange between Britain and northern Ireland."