In a video statement, GMB General Secretary Tim Roache says the union's members in manufacturing, retail and other sectors face uncertainty because the British government has yet to negotiate a deal with the EU.
Writing in the popular Sunday newspaper, the British Prime Minister said she would not be pushed into compromises over Brexit that weren't in the national interest, seeking to allay fears among some in her Conservative Party that she would cave in to Brussels' demands in negotiations.
"In the summer of 2016, millions came out to have their say", she wrote in the Sunday Telegraph.
Meanwhile, 52% of voters in Northern Ireland said they would vote for a united Ireland outside of the UK after Britain leaves the European Union, with 39% favouring the province staying part of the UK while 7% did not know and the remainder said they would not vote.
Johnson fumed in a newspaper column that May's proposal to retain close economic ties with the European Union after Brexit would leave Britain locked in the trunk of a Brussels-driven vehicle with "no say on the destination".
"The negotiations are taking place with the commission, we have always respected that fact", said the PM's spokesman.
"Michel Barnier, the EU's chief Brexit negotiator, "made clear" to MPs on the Brexit select committee that the Chequers plan is "not acceptable" during a meeting in Brussels".
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"The nature of the financial settlement, as has been set out in the withdrawal agreement, is contingent upon us agreeing the deal as a whole", he said. What we need at this time is serious leadership with a serious plan. We have suffered catastrophic failure in all four engines and are losing altitude at a rate of 10,000 feet a minute.
Another MP, Heidi Allen, told the BBC's Newsnight some of her fellow pro-EU Conservatives viewed Chequers as a "complete non-starter" but others, like her, were prepared to give it a "little bit longer".
He also defended the UK's plans for the possibility of no deal being reached, which included publishing 25 notices last month offering advice on how best to prepare for such a scenario, saying: "The UK will be ready for Brexit, deal or no deal".
The plan infuriated Brexit-backers in May's Conservative party including Johnson, who quit the government in protest.
Eurosceptics are drawing up an alternative deal they hope Johnson and Davis will support when it is unveiled before the party's annual conference later in September, reports said.
Responding to Mr Barnier's remarks, a Government spokeswoman said: "We are confident that we have put forward a proposal that is precise, pragmatic and that will work for the United Kingdom and the EU".
Since the publication of the government paper detailing the government's proposals, the so-called Chequers plan unveiled by May, British ministers have had more than 60 ministerial engagements with their counterparts across Europe, said Raab.