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A cross-party deal for a softer Brexit inched closer today when one of Jeremy Corbyn’s closest allies said Labour could support “some element” of European free movement.

Shadow business secretary Rebecca Long-Bailey indicated her party could be flexible in the interests of securing “impediment-free” trade with the EU’s single market of 500 million customers.

On the Conservative side, former chancellor Kenneth Clarke, the Father of the House of Commons, warned Theresa May that a deal with Northern Ireland’s DUP would not rescue her promise of a so-called hard Brexit because the Tory party would split.

Senior MPs and ministers believe there is no clear majority for any of the official positions advanced by the main parties in their manifestos, forcing compromises to avoid a stalemate.

Tory MPs and ministers who want a deal to protect the economy and jobs are looking to Chancellor Philip Hammond to give a lead in his annual Mansion House speech tomorrow. He has argued in private for Britain to stay in the borderless customs union in order to maximise trade with the EU, Britain’s biggest export market. Ms Long-Bailey said the Prime Minister would have to seek consensus by talking to other parties.

She told BBC Radio 4: “We accept the fact that, if we are going to have impediment-free access to the single market, then there will have to be some element of free movement.

“I think we know that, the Conservative party know that, but the specific points are open to negotiation.”

Downing Street said talks between Mrs May and the 10-strong Democratic Unionist Party were “ongoing” this morning. A deal would allow Mrs May to pass the Queen’s Speech in return for concessions, which are thought to include an economic package for Northern Ireland. A senior Conservative source said: “We are making a lot of progress.”

However, Mr Clarke scoffed at the idea that the DUP’s support would allow her to carry the Commons with her on a hard Brexit, because Tories were divided on key negotiating points.He said: “You cannot carry out this negotiation on the basis that every aspect of it is going to be negotiated with the DUP to get their vote in support of it, and then you are going to try to get the entire Conservative prty to agree with each other on whatever you have tried to negotiate. Both parties, major parties, are hopelessly split on the issue.”

Pressure on Mrs May to change her approach also came from Tory predecessors David Cameron and John Major. Mr Cameron said Parliament “deserves a say” and urged the Government “to consult more widely with the other parties” on how best to achieve a deal. He also highlighted the role of Scottish Tories, led by Ruth Davidson, who are opposed to a hard Brexit.

Speaking in Paris last night, Mrs May stressed that Brexit would happen and the timetable remains on course.

She said: “I think there is a unity of purpose among people in the United Kingdom. It’s a unity of purpose, having voted to leave the EU, that their Government gets on with that and makes a success of it.”

At a joint press conference with her, new French president Emmanuel Macron said the door was still open for the UK to remain in the EU. But EU Brexit co-ordinator Guy Verhofstadt said Britain will lose the rebate won by Margaret Thatcher and its single currency opt-out if it tries to stay in. European Commission president Jean-Claude Juncker said the EU needed to work more closely on defence and refugees. @JoeMurphyLondon