Labour has reached agreement with the unions on its flagship workers’ rights proposals after general secretaries demanded the party commit to no further weakening of the original plans. One of the key critics of changes, the Unite general secretary, Sharon Graham, said the unions had “been listened to and the workers’ voice heard in what she described as a “red line” summit with Keir Starmer on Tuesday. The Labour leader and his senior team met union leaders for the crunch meeting to thrash out a deal on the plans, which were originally agreed last July. One union source told the Guardian the general secretaries had presented a united front and told the Labour leader he should agree to return to the language agreed at the national policy forum last summer. Another meeting will take place in three weeks’ time to confirm the changes. In a joint statement after the talks, Labour and the unions said: “Labour and the affiliated unions had a constructive discussion today. “Together we have reiterated Labour’s full commitment to the ‘New deal for working people’ as agreed in July. We will continue to work together at pace on how a Labour government would implement it in legislation.” It means the deal agreed last July, which already represented what critics described as a “watering down” of several of the original proposals, is now the party’s agreed position. Unite and the Fire Brigades Union (FBU) had been among the unions to have publicly criticised what they termed a “betrayal” of the previous promises to overhaul rights at work. The Guardian understands that concerns about the draft document extended well beyond those unions which had been openly critical. Senior Labour figures are also understood to have been bruised by the leaking of the internal draft to newspapers including the Guardian. The general secretaries convened on Tuesday morning before the lunchtime meeting with Starmer, the deputy leader, Angela Rayner, the shadow chancellor, Rachel Reeves, party chair, Anneliese Dodds, shadow business secretary Jonathan Reynolds, and the shadow chief secretary to the Treasury, Darren Jones. The majority of unions affiliated to Labour had privately raised concerns about the latest draft of the document that included several changes to the proposals, including the speed and methods of the changes. “We believed that the party had agreed all of these measures with us at the national policy forum last summer,” one union source said. “We are trade unionists and we know when we make an agreement – we don’t expect to be then given a different draft months later and be told, actually this is what’s going to happen.” Another union official said: “There are those who want to make their case publicly, but the concerns are shared privately by most unions. It’s not only about consultations, which is how the Labour party have tried to frame this; there are promises that were made, such as on sick pay, which have gone completely.” Dave Ward, the general secretary of the Communication Workers Union, told LBC the deal “will be implemented as we agreed previously. Keir’s made it very clear how transformational that will be for working people. “We’ve got the position we all want … this will be the biggest difference in rights the country has ever seen in decades; it will be a flagship policy for the general election. We need to shift the balance of forces in the world of work back towards working people, that’s the only way you’re going to grow the economy.” Labour has proposed sweeping overhauls of workers’ rights, including maternity and sick pay, day-one protection against unfair dismissal, bans on zero-hours contracts and fire and rehire practices, fair pay agreements and union access. One of the subsequent changes that angered unions was allowing workers to stay on zero-hours contracts if they preferred – which they said would be a loophole for exploitation. A key point of contention was over changes to the language on fire and rehire, which Labour had committed to banning in law. The leaked draft shared with unions says Labour would “replace the inadequate statutory code brought in by the government with a strengthened code of practice and reform the law to provide effective remedies against abuse”. But the document also says it is “important businesses can restructure to remain viable … when there is genuinely no alternative”. A Labour source said before the meeting the party defended those changes. “If a company is faced with changing terms and conditions or mass redundancies then there needs to be an exception to protect jobs,” the source said. “Protecting jobs is always the final priority. Even Barry Gardiner in his private member’s bill [on fire and rehire practices] had similar exemptions.”