May was visiting Scotland, England, Northern Ireland and Wales during her day-long tour, aiming to shore up support for the government's Brexit strategy.
"I am determined that as we leave the European Union and in the years ahead, we will strengthen the bonds that unite us", May said.
May stated that "we are absolutely committed to ensuring that there is no hard border".
"What formalities companies now trading intra-EU will face at the UK-EU border are still unclear, " said Doherty.
The complex process of leaving the European Union has spawned its own jargon - cake philosophy, divorce bill, cliff edge, ambitious managed divergence, cherry-picking - while the influential group of those who voted to remain in the European Union continues efforts to block Brexit in Parliament, courts and elsewhere.
Since formal negotiations began between the two sides last June, an agreement has been struck on a Brexit "divorce bill" - but the crucial issue of how they will trade together has yet to be settled.
Carwyn Jones, First Minister of the Welsh Assembly, said the prime minister did not have a clear plan for a UK-EU relationship after the "transition period" ends.
He told BBC Radio 4's Today programme the tests were "nowhere near being met" and insisted Labour would not vote for the deal unless "the government are sensible and they negotiate properly".
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Kicking off in Scotland, the Prime Minister will visit textile workers at a factory in Ayrshire, before travelling to Newcastle to meet with a local parent and toddler group.
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".
According to Wednesday's poll, by ComRes for the Daily Express, only 29 percent are "optimistic" that their household "will be better off" after Brexit, and 35 percent are optimistic that the United Kingdom will be able to negotiate a trade deal with the European Union before leaving. It's a future in which we trade freely with friends and partners across Europe and beyond.
The prime minister, speaking on a whistle-stop tour of the UK's constituent nations to mark a year until Britain formally leaves the European Union, evaded the question.
Later this year, Theresa May will put an outline of the Brexit deal to Parliament for its approval.
During her visit to Bangor, Northern Ireland, on Thursday, she repeated her "commitment to avoid a hard border" between the United Kingdom region and the Republic of Ireland, and to "protect" the 1998 peace agreement.
"There is still a real chance that we should be able to choose, if that's what we want, a different path and not go down the Brexit route", she added.
With the Irish border remaining a sticking point, May said she will promise to ensure "no new barriers are created within our common domestic market".