The meltdown at People’s Vote is poised to worsen as staff plan to confront the campaign’s chairman, Roland Rudd, about the sacking of two senior executives and further moves are expected in an attempt to oust Peter Mandelson and his allies from the board.

The campaign for a second referendum is set for a showdown on Tuesday morning after around 35 staff walked out in support of James McGrory, the campaign director, and Tom Baldwin, the communications director, who were fired by email by Rudd over the weekend.

Allies of Rudd have been trying to change the management of People’s Vote and merge its parent organisation, Open Britain, with other pro-EU groups. Meanwhile, a group including McGrory, Baldwin, Lord Mandelson and others have been fighting to keep the organisation focused on winning the argument for a second EU referendum.

Rudd is expected to move next to remove Mandelson, his former friend of 30 years, from the board of Open Britain. Mandelson has tried to resist Rudd’s growing control over the organisation and efforts to change the senior staff.

During a telephone meeting of directors on 9 October, Rudd received support from six other directors to get rid of four People’s Vote directors – Mandelson, McGrory, Will Straw and Joe Carberry. They are due to be removed as directors next week.

Mandelson told the Guardian: “Roland Rudd is like the captain of the Titanic demanding the passengers show him more respect as the iceberg carves open the hull and water gushes into the bowels of the ship.”

Trevor Phillips, the former head of the equalities and human rights commission, is understood to have questioned at the meeting why he was the only director among those supporting Mandelson to survive the cull. “Is it because I is black?” Phillips asked Rudd, and he insisted the exchange was minuted.

In an email sent on Monday to fellow directors, Phillips wrote that the organisation was now a laughing stock and was failing supporters of a second referendum.

Rudd, in a series of broadcast interviews, denied that a row was overtaking the organisation. He said: “I think we are tantalisingly close to getting [a people’s vote] or a confirmatory vote on the government’s deal. Parliament has come closer to us than ever before and because of that we need to stay focused on the main prize and try not to fuel rows outside when we have to reverse this Brexit madness.”

Allies of Rudd said Mandelson and Alastair Campbell, Tony Blair’s former director of communications, had previously tried to remove him as chairman. Emails leaked to the Mail on Sunday a week ago showed Campbell suggesting: “I do not see how this gets done without a public battle and it should happen soon and be fast and brutal.”

The latest bout of infighting exploded into the open on Sunday night after the Open Britain board under Rudd’s chairmanship voted seven to three in favour of removing Baldwin and McGrory. Rudd then emailed staff saying McGrory and Baldwin were leaving their roles with immediate effect.

He said the organisation needed a new structure and a former Labour campaigns adviser, Patrick Heneghan, would be installed in their place to work on “building a new campaign, more professional and more in touch”.

Rudd, the brother of the former cabinet minister Amber Rudd, was due to speak to staff in the office at 9am on Monday, but he sent Heneghan in his place and did a round of broadcast interviews in which he claimed “there is no row”.

After listening to Heneghan, dozens of staff walked out of the office on London’s Millbank and reconvened at a cafe in a move to support McGrory and Baldwin. One of them, Richard Brooks, who is part of For Our Future’s Sake, said FFS was “not consulted on these changes [and believes] that they are wrong and tantamount to a corporate coup”.

Baldwin said both he and McGrory intended to turn up to work as usual on Tuesday and attend a second meeting convened by Rudd at 10am to speak to staff.

Baldwin said: “Does someone who does that ahead of this week in politics on Brexit really care about a people’s vote and scrutiny of Boris Johnson’s Brexit? Or is it someone who is trying to gain complete control over the campaign? I think anyone who cares about remain and stopping Boris Johnson’s Brexit should think very hard whether they want to have anything to do with someone like Roland Rudd in any capacity.”

However, they could face difficulty trying to get into the office, as a People’s Vote source said their passes have now been cancelled and security would prevent them from entering. Allies of Rudd said the move was necessary to move the campaign into a new phase and there had been questions over the competence of the fired staff members.