Jeremy Corbyn and his inner circle are considering a frontbench reshuffle that could see the shadow foreign secretary, Emily Thornberry, moved as a punishment for insisting that the party must back a second Brexit referendum, according to several senior figures in the party.

There is also growing support from some of Corbyn’s allies, including union leaders close to the leader’s office, for a new contest to be held that could see Tom Watson replaced as deputy leader, following his persistent backing for a public vote on the UK’s exit from the EU.

Sources inside Corbyn’s office said last night that there were “all sorts of mischievous rumours” being put about, but did not confirm – or rule out – imminent changes to the party’s top team. “They are very angry with Emily and are out to get Tom,” said one shadow cabinet source. “That has been incredibly obvious over recent days.” Another senior source said: “There is talk of petitions going round local parties, particularly to rally support for a deputy leadership contest. This would require more than 50 MPs to back it to get off the ground. They may want to do it, but it almost certainly won’t work.”

Thornberry was humiliated last week when Corbyn’s office decided to ditch her as the stand-in at prime minister’s questions in favour of shadow business secretary Rebecca Long-Bailey, who is a close ally of both Corbyn and the shadow chancellor, John McDonnell.

The decision was taken, according to insiders, because Thornberry had blamed the party’s poor showing in the European elections on its ambiguous position over a second referendum and called on the party to give unequivocal backing to a second vote in which the party would campaign for Remain. One idea being floated by Corbyn supporters, say sources, is that Thornberry should swap positions with the shadow home secretary, Diane Abbott, to help ensure that Thornberry is removed from direct involvement in strategy around Brexit. “They have been trying to do this for weeks, but Diane refuses to move,” said one senior MP.

Shadow ministers also believe that some in Corbyn’s office want to remove Keir Starmer as shadow Brexit secretary, because he had led calls for the party to back a second referendum. But it is thought Corbyn is unlikely to risk a move which MPs believe could lead to Starmer’s resignation.

Pressure for a contest to select a new deputy has come from Dave Ward, general secretary of the Communication Workers Union and an ally of Corbyn. He is understood to have the backing of Unite’s general secretary, Len McCluskey.

There was intense relief at the top of the party on Friday morning when Labour narrowly retained the marginal seat of Peterborough, seeing off a challenge by Nigel Farage’s Brexit party. Labour’s candidate, Lisa Forbes, won 10,484 votes, beating the Brexit party candidate, Mike Greene, by 683 votes. The Conservatives were beaten into third place.

Corbyn is expected to address the parliamentary Labour party tomorrow about Labour’s performance in the European elections, which saw it lose half its seats.