A group of prominent Labour politicians including four frontbenchers and former cabinet ministers have raised the pressure on Jeremy Corbyn to fight for membership of the single market as they launched an attack on the threat of an “extreme Tory Brexit”.

Chuka Umunna, Stella Creasy, former Northern Ireland secretary Lord Hain and Lucy Anderson, a supporter of Corbyn, are among the 50-plus politicians who have said the single market represents the best hope of ending years of Tory austerity.

The intervention comes as Labour’s leadership is forced to end months of apparent ambiguity over the party’s stance on key elements of Brexit talks.

Senior figures including John McDonnell, the shadow chancellor, and Keir Starmer, the shadow Brexit secretary, have ruled out “full” membership of the single market – saying it would be lost simply through departure from the EU – but suggested Britain could try to retain many of the benefits.

Today Umunna, the former shadow business secretary, told LabourList the party must exploit the Tories’ weakness in the Commons to fight an ideologically-driven hard Brexit.

“The Tory Brexiteers have been influential in national debate and secured a Leave vote in part because they got organised. We need to do the same if we are to oppose their job destroying form of Brexit – one that seeks to dump people’s social protections and turn the UK into Europe’s sweatshop.

“Given the arithmetic in the House of Commons, every MP has more influence than in the last Parliament and we intend to use it. The Tory frontbench carry on as if they alone will determine the deal we reach with the EU but they can’t do anything unless they have the numbers in the Commons and Parliament signs off on the deal – this PLP group will use that influence to secure the most socially just outcome through this process”

Last night the group of Labour MPs, 11 MEPs, peers and an ex-trade union leader praised Corbyn’s “jobs first” approach to Brexit talks but called on the party to seek single market membership Britain has left the EU.

“If Britain stays in the single market, we will continue to benefit from EU laws and court judgments that outlaw discrimination in the workplace; deliver vital rights to workers on holiday pay, maternity and paternity leave, the right to join a union, and much more; protect our natural environment from pollution; and keep workers safe through stringent health and safety requirements,” they wrote in The Guardian.

“Large multinational companies work across borders to maximise their profits to often reduce these protections; the next Labour government, as a member of the single market, can work with other European countries to resist this and advance social justice. If we leave the single market, and ask for mere ‘access’, we will be compromised in achieving these goals.”

The letter is unusual because of the breadth of opinion it represents, from single market campaigners like Umunna and new MPs like Darren Jones to John Monks, a former general secretary of the TUC, and frontbenchers Daniel Zeichner, Thangham Debonnaire, Ruth Cadbury and Andy Slaughter.