"What formalities companies now trading intra-EU will face at the UK-EU border are still unclear, " said Doherty.
The British prime minister kicked off a whistle-stop tour of the United Kingdom with a visit to a weaving firm in Ayr, where she said she expected to be able to negotiate a deal with the European Union allowing a "good trading relationship" in future.
But first, May has to agree a deal in Parliament, with a vote expected in October.
Labour's shadow chancellor John McDonnell accused the British government of being in "chaos" over Brexit, following a series of defeats in the House of Lords on its flagship EU Withdrawal Bill.
On Wednesday, shadow foreign secretary Emily Thornberry faced criticism from within her own party for saying Labour MPs would probably approve the government's "blah, blah, blah" deal that would pass Labour's six tests - which included maintaining the benefits of the single market and customs union.
"By pursuing a disastrous hard Brexit, regardless of the cost to jobs and living standards, Theresa May and the Tories have shown they think they can now do anything to Scotland and get away with it", said Mr Russell.More news: Nvidia Declines After Suspending Self-Driving Car Testing
Media captionWith a year until our departure, what do voters make of the Brexit progress so far?
Speaking ahead of her trip, she vowed to regain control of "our laws, our borders and our money" and that the UK will "thrive as a strong and united country that works for everyone, no matter whether you voted Leave or Remain".
Mrs May is facing conflict with devolved administrations in Scotland and Wales, who want powers from Brussels repatriated to them rather than London.
Each of the devolved nations will see an increase in their decision-making powers.
The UK is to stick to the European Union recycling targets, despite previous opposition, and is set to back the goal of recycling two-thirds of waste by 2035, The Guardian has reported.
And Theresa May's message is suitably upbeat.More news: Six year old free trade agreement overhauled by USA and South Korea
"Today, one year until the United Kingdom leaves the EU and begins to chart a new course in the world, I am visiting all four nations of the Union to hear from people across our country what Brexit means to them", May said ahead of her tour.
"I believe there is a bright future out there once we've left the European Union", May said during her visit to Bangor in Northern Ireland.
She argued that "it's a future in which we trade freely with friends and partners across Europe and beyond", and the United Kingdom would thrive.
While there she also addressed the issue of the border between Northern Ireland and the Republic of Ireland, one of the most crucial and contested issues to come out of Brexit.
She replied by saying her government was having "good discussions" with SNP ministers on the issue, adding: "We have put forward proposals as to how this issue can be resolved".More news: John Bolton's plan to be Trump's "enforcer"
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