Leading figures from the labour movement have stepped up the pressure on Theresa May’s uncertainty over Brexit after she pledged Britain would trigger the formal negotiation process by the end of March.

Emily Thornberry said the commitment was “meaningless” unless the prime minister could answer fundamental questions over trade and relations with the EU while the head of the TSSA union warned that he and his colleagues would resist efforts to turn Britain into an “offshore sweat-shop or tax haven”.

They spoke out as the Tories gather for party conference in Birmingham.

The Government’s annual shindig kicked off yesterday with a pledge from May to begin the article 50 negotiations over Brexit by April. This could put Britain on course to leave the EU by summer 2019. May tried to strike a decisive tone – claiming ministers would “get on with the job of enacting the referendum result – but faces increasing questions over her failure to spell out any details beyond the “Brexit means Brexit” soundbite.

Thornberry, shadow foreign secretary and shadow Brexit secretary, lambasted May over the failure to answer “fundamental questions about what deal Britain is going to propose for our future relationship with the EU, what the plan is to secure that deal, and what we will do if it fails”.

She added: “This is exactly the same mistake David Cameron made with his proposed renegotiation last year: working to an artificial, self-imposed timetable; with a flawed Plan A of what he wanted to achieve; and no Plan B whatsoever. Unless Theresa May starts spelling out the government’s plan on free trade, on free movement, on budget contributions, and a host of other issues, we will have to conclude she is only interested in achieving headlines not providing solutions.”

Manuel Cortes, general secretary of the TSSA, said the Tories were neglecting the key areas where investment was needed to boost the economy.

“The trade union movement will not allow May to turn Britain into an offshore sweat-shop or tax haven. Our country’s future wealth will not be built on more Tory zero-hour contracts. Our economy and our people urgently require investment in public infrastructure programmes, social housing and educating our young people with the transferable skills needed for to transform future Britain into a high-skilled, high-tech industrially smart economy. Brexit cannot be left to undemocratic Tories to wreak more neo-liberal havoc. We will hold them to account.”

Stephen Kinnock said: “The Brexit process will give this government more power to re-shape Britain than any government has had since the Second World War. And yet what Brexit means is still unclear, and the government has no specific mandate for its negotiating position, assuming that it has one.

“That is why the prime minister must make clear her plan for Brexit to the British people and make it a national plan, not just a Conservative one. This process must be about determining how Britain leaves the European Union, not how Mrs May deals with her backbenchers.”