The Prime Minister is in Northern Ireland on a two-day visit focusing on Brexit and the political stalemate in the country where the devolved Stormont assembly has been suspended since January of a year ago.
Still reeling after her Brexit plan triggered the resignation of senior members of her cabinet, May flew to Northern Ireland on Thursday for a two-day visit to see up close the troubled British region's frontier with EU-member Ireland.
May narrowly avoided a defeat in parliament at the hands of the pro-EU lawmakers from her own party in Tuesday's vote, helped by four opposition Labour lawmakers who went against their party to support the government.
May will tell an audience of business leaders and politicians that the European Union proposal is in breach of the Belfast Agreement because it would create a barrier between Northern Ireland and Great Britain and leave the people of Northern Ireland "without their own voice" in trade negotiations.
Before leaving the factory, May met local woman Delma Käthner, who told her she was "bionic".
Theresa May faces a fresh Commons battle over Brexit just hours after Tory civil war pushed her customs legislation to the brink.
Within days Michael Heseltine challenged Mrs Thatcher for the Tory leadership and she was eventually ousted and succeeded by John Major.
Q&A What is regulatory alignment?
Mrs May said she is committed to keeping a soft border, and her Chequers plan pits forward the idea of sticking to European Union rules on the trade of goods - in part to avoid a hard border. Speaking at the IQVIA event, he suggested that post-Brexit the UK's MHRA regulator should become a specialist regulator in cutting edge areas such as advanced medicines, in order to attract the sector to the UK.
After Tuesday's vote, the trade bill, which shifts to United Kingdom law the existing European trade agreements, will go to the House of Lords that will study it after the summer recess.
"Will the refusal to allow Aer Lingus planes flying to and from Belfast, to fly across Ireland represent a hard border and be a breach of the Belfast Agreement?"
Brexiteers believe that keeps Britain too close to the European Union, while pro-Europeans think it fails to protect the country's dominant services sector, among other gripes.
The British government wants to retain the ability to sign trade deals independently of the EU.
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However, in March the Northern Ireland Affairs Committee expressed its concern over progress, pointing out the absence of a technical solution anywhere else in the world that could be adopted to render the border invisible.
Britain's Prime Minister Theresa May visits Belleek Pottery, in St Belleek, Fermanagh, Northern Ireland, July 19, 2018.
"If I can say to her, I know that she wants us to talk about the positives of Brexit and I agree with her, we should be talking about the positive future for this country".
"Our job is not to deal with Brexit in theory, but to make a success of it in practice for all of our people".
Ms Greening, who resigned after the cabinet reshuffle in January, said the referendum should offer a first and second preference vote so that a consensus can be reached.