Labour’s deputy leader, Tom Watson, is promising to “ensure all voices within the party feel they are being heard”, as he convenes a new centre-left grouping of MPs, widely regarded at Westminster as a rival power base to Jeremy Corbyn’s.

Watson has made a series of pointed public interventions since a group of seven MPs announced that they were leaving the Labour party to form the breakaway Independent Group (TIG). In particular, he urged Corbyn to reshuffle his shadow cabinet, and to take personal oversight of the handling of antisemitism cases.

But with little sign of the Labour leader making any concessions to the splitters, and the antisemitism crisis in the party deepening, Watson plans to bring like-minded backbenchers together in what is being called the Future Britain Group at a meeting on Monday.

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In the invitation sent to parliamentary colleagues, he said: “I believe the time is right to restate our social democratic values once again in order to address the challenges our country faces. Life after Brexit and Britain’s relationship with the world, automation, the housing crisis, inequality, climate change and more.” The language echoes that used by MPs from the Independent Group, including Chuka Umunna.

The deputy leader is regarded as a pivotal figure, whose involvement in any new parliamentary grouping would significantly increase its political influence. But he insists he is going nowhere; and friends say he is too tribally loyal to Labour to join a grouping alongside former Conservative MPs.

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“For as long as I’ve been in Labour, our culture of pluralism and diversity of voices on the left has been our great strength,” Watson said. “As deputy leader, it’s my job to do everything I can to hold the party together and ensure we are ready to government,” he said.

Corbyn has approved the plan for the creation of the new group, which the pair discussed when they met this week.

Labour already has a shifting cast of political groupings, including the soft-left Tribune group and the socialist Campaign Group, of which Corbyn and his closest ally, John McDonnell, are longtime members.

When Labour was in government during Tony Blair’s premiership, McDonnell regularly produced alternative budgets, setting out policies that were more leftwing than Gordon Brown’s.

Play Video 2:27 Tom Watson: Labour must tackle antisemitism to prevent more MPs leaving – video

But the fact the Future Britain Group will meet before the weekly gathering of the parliamentary Labour party will raise fears that Watson is creating a caucus within the wider party, which could agree policy positions and seek to work together to exert pressure on the leadership.

After the departure of the TIG MPs, McDonnell promised a “mammoth listening exercise” to take on board the concerns of MPs. But other senior Labour figures felt he had gone too far in accommodating the complaints of Umunna, Chris Leslie and the other breakaway MPs.

When Corbyn was asked the day after the split whether he would heed Watson’s voice and broaden out his shadow cabinet, he said: “Anyone who does not feel consulted is not taking up, in my view, the opportunities that are available, at all times, to do that.”