Almost a fifth of the UK's food and drink exports go to the Republic of Ireland and in March industry bodies from across the British food and drink sector wrote an open letter to various government departments calling for "frictionless" tariff-free trade with Ireland to continue post-Brexit.
"We made the case to her that we would oppose any deal that undermined the Good Friday Agreement", he said.
"Both parties are committed to strengthening the union, combating terrorism, delivering Brexit and delivering prosperity across the whole of the country", the source said.
"The danger is that however much any government tries they will not be seen to be impartial if they are locked into a parliamentary deal", 1990s Conservative prime minister John Major told BBC radio.
Though on the surface, Thursday's meeting with Northern Irish parties is aimed at breaking the logjam in forming a new cross-party regional government in the province, May needs broader acceptance of a Conservative-DUP deal.
Under the proposed deal, the DUP would likely support May's Conservatives on big issues such as the budget, Brexit and defence legislation on a vote-by-vote-basis.
"On the one hand, Arlene Foster tells us she does not wish to see a hard Border and on another Ian Paisley tells us the DUP position supports "properly and fully leaving the EU customs union", he said.More news: Another deadly explosion rocks Kabul, 19 feared dead, several injured
The nationalist Sinn Fein and SDLP and the cross-community Alliance have all made clear Northern Ireland Secretary James Brokenshire can not chair the ongoing process to restore power-sharing at Stormont due to the perceived conflict of interest.
She added: "I think it is regrettable that Northern Ireland is the only part of the United Kingdom where loving, same-sex, couples cannot get married as they can in England, Wales and Scotland".
The Irish government statement said there was agreement on the importance of a functioning executive in the context of the Brexit negotiations due to start next week.
However, the survey was conducted at the end of previous year, just prior to the collapse of devolution and two polarising elections which have seem tribal politics come to the fore and seen both the DUP and Sinn Fein consolidate their positions as the lead parties of unionism and nationalism respectively.
Brexit is another complicating factor in the mix.
Such is the collapse of May's authority that her entire Brexit strategy is being picked apart in public by her ministers, her lawmakers and her allies on the eve of formal negotiations which begin in Brussels today at 0900 GMT.
The Common Travel Area is an open borders area comprising the Republic of Ireland and Britain.
He said: "A lot of the things people are concerned about are devolved to the Northern Ireland Assembly and I don't think the social matters will be central issues".