Theresa Villiers, the Northern Ireland secretary and leave supporter, has rejected Sinn Féin demands for a referendum on the region’s position inside the UK after Brexit.

As towns, cities and communities, such as Newry, that voted to remain in the EU absorb the Brexit shock, Villiers said there were no grounds to hold a border poll on a united Ireland.

Theresa Villiers speaking to the press on Friday. Photograph: Ben Stansall/AFP/Getty Images

In a brief statement on Friday, Villiers said: “The Good Friday agreement is very clear ... There is nothing to indicate that there is majority support for a poll.”

Under the rules set down by the 1998 Good Friday peace deal there cannot be a poll on Irish unity or remaining within the UK unless the majority of political representatives of both communities in Northern Ireland demand it.

Given the Democratic Unionist party’s lack of enthusiasm for a border poll it is unlikely the British government would grant one.

In Newry, a frontier city with the Irish Republic that is adjacent to the republican South Armagh redoubt, the overwhelming majority of businesspeople and shoppers expressed concern about what Brexit would mean for them.

Declan McChesney is the third generation of his family to run Cahill Brothers women’s shoe shop in Newry’s Hill Street. The head of the 132-year-old business also runs an enterprise importing high-grade fashion shoes from Italy, Spain and Portugal.

“Personally speaking I am on the floor over this Brexit vote,” McChesney said as his six staff prepared for day one of their summer sale season.

“If you take my shoe import business, what am I going to do now if they impose border or customs control just a couple of miles south on the border? I sell the imported shoes both in Northern Ireland and the Republic. Will I have to put special markings on the shoes I sell into the non-EU north when I am stopped by customs officers in the near future?

“About 30% of my business in this shop comes from the south and I am worried that if there is a crisis between the pound and the euro will our products be too expensive for my southern customers? We have survived as a family business two world wars, the aftermath of the Easter Rising and the modern Troubles. Now we have a new crisis that never needed to happen here after all that we survived. It is deeply depressing.”

McChesney added that it would be “highly dangerous especially for a young generation who never knew about the Troubles” if the Newry area faced another “hard border” of vehicle checks and enhanced security.

Sheltering from a torrential downpour in the front of a Menary’s store also on Hill Street was Shirley Connolly, 46, who lives on the southern outskirts of Newry and who can walk into Co Louth in the Irish Republic in under five minutes.

Connolly shared McChesney’s gloom over the Brexit outcome. The volunteer childcare worker said: “My family owned a haulage business and every time they moved their lorries from Dublin docks up into Northern Ireland there would be tailbacks just north of Dundalk as they tried to get into Newry, because they used to check all the vehicles, both customs and security checks. It would be terrible if we returned to those days again. That is why I voted to remain like almost everybody in Newry. We knew what it is like to have a border like that and we don’t want it back.”

Irish nationalist politicians on both sides of the only land frontier the UK now shares with an EU state have claimed that any border fortifications would become a target of dissident republicans aiming to destabilise Northern Ireland.

Conor Patterson runs five business parks stretching from Kilkeel on the South Down coast to the South Armagh end of Newry City. Patterson said any reinforcement of the border could have an adverse impact on the local economy.

“During the Troubles in the early 1970s this place held the record of the highest unemployment in the UK with nearly 30% out of work but today it stands below the Northern Ireland average at 6%. This turnaround was achieved partly by the peace process but also due to massive investment from the EU in our infrastructure.

“Our rail stations were rebuilt thanks to millions from the EU as were the bypass around Newry. Is Arlene Foster [the first minister] seriously telling us that the British Tories who are committed to the economic survival of the fittest and are totally opposed to state intervention and regional policy going to fill the gaps left by no longer getting EU support?

“I fear they have no plan or pathway as to how places like Newry are going to cope outside the EU,” Patterson said.