Two ministers quit the government in protest on Wednesday as Theresa May suffered a furious Conservative backlash after opening the door to negotiations with Jeremy Corbyn for a Brexit deal.

Eurosceptic MPs reacted with horror to the prime minister’s offer to work with Labour following Tuesday’s marathon cabinet meeting.

Brexit: Junior minister resigns over May's 'grave error' in seeking deal with Corbyn – live news Read more

Nigel Adams, a government whip and under-secretary of state for Wales, quit in protest at May trying to “cook up a deal with a Marxist”.

Chris Heaton-Harris, a Brexit minister, also resigned. “I simply cannot support any further extension to article 50 and this obviously means I cannot stay in government,” he said. “I truly believe we should have honoured the result of the 2016 referendum [by leaving EU on 29 March].”

Their departures came as senior Eurosceptics, including Boris Johnson and Jacob Rees-Mogg, expressed outrage at the idea that May would be willing to work with Labour.

May was challenged directly by a string of Tory MPs at prime minister’s questions about the decision to discuss the idea of a softer Brexit, which could involve tearing up a manifesto commitment not to pursue a customs union.

Iain Duncan Smith, the former Conservative leader, described May’s offer of talks as a shocking betrayal of Brexit. Writing in the Telegraph, he said: “The spectre of Corbyn lording it over us in a prime ministerial way as he wrecks Brexit makes my blood run cold and fear for my party and my country.”

Even some normally supportive MPs were incredulous, with Caroline Johnson standing at PMQs to say she backed the deal, but adding: “If it comes to the point when we have to balance the risk of a no-deal Brexit versus the risk of letting down the country and ushering in a Marxist, antisemite-led government, what does she think, at that point, is the lowest risk?”

The fury was so great that some pro-Brexit MPs were discussing ways to remove the prime minister, while circulating a motion censuring May’s action and proposing to dock half the pay of cabinet ministers.

May could only be removed now by MPs through a vote of confidence in the government, which would be given parliamentary time if tabled by Corbyn.

An attempt to remove her in December, led by Brexiters who sent letters of no confidence to the 1922 Committee, the powerful Tory backbenchers’ body, failed, and cannot be repeated for another eight months.

Pro-Brexit ministers were more circumspect, holding off while they waited for the outcome of May’s talks with Labour. The so-called “Pizza Club” of senior government Brexiters, such as Andrea Leadsom and Penny Mordaunt, were understood to be angry, but no decisions had been taken about the way forward.

May wrote to all Conservative MPs on Wednesday morning to explain her decision, and blamed the Democratic Unionist party and leave-supporting backbenchers for failing to support her deal.

'Jezz the two of us': what the papers said about May's overture to Corbyn Read more

“The question is, how can we get parliament to ratify the deal? The government would have preferred to do so based on Conservative and DUP votes. But, having tried three times, it is clear that is unlikely to happen,” she wrote. “I realise some of you will be concerned about the government discussing the way forward with the opposition. However, with some colleagues unwilling to support the government in the division lobbies, this is the only way to deliver the smooth, orderly, Brexit that we promised and for which the British people voted.”

Government ministers were careful not to rule out any options as May and Corbyn met to see if they could find common ground.

Stephen Barclay, the Brexit secretary, did not rule out giving in to demands for a second referendum, telling MPs: “I don’t think we should have a second referendum because it takes us back to square one, [it’s] my personal view. But the prime minister will have discussions and we will see where they lead.”

However, he also suggested there could be limited appetite for a compromise on the Conservative side, while insisting the talks were being pursued in good faith. “I personally think a customs union is highly undesirable. We’re not setting preconditions, but nor is this a blank cheque,” he told BBC Radio 4’s Today programme.

To those Tories complaining about May’s move he said there was a “remorseless logic” to reaching out for Labour votes when 35 Conservatives had refused to back the prime minister’s withdrawal agreement three times.

What is Theresa May's new plan for Brexit? Read more

Eurosceptics appeared to be deeply shocked by May’s move, as many of them had been hoping that she would pivot towards a no-deal Brexit after the successive failures to get her withdrawal agreement through the Commons.

Stewart Jackson, a former Tory MP and Brexit adviser, suggested a fresh move be made against May. “Isn’t it time Graham Brady and the executive committee of the 1922 reviewed the rules and instigated a fresh leadership ballot? May has no mandate to pursue the Corbyn pact.”

Some ERG members demanded that the 1922 Committee should hold an indicative vote of no confidence in the prime minister.

Mark Francois, the ERG’s deputy chair, said members of the 1922 Committee of backbench Tory MPs were told by the chair, Sir Graham Brady, that the executive committee had decided not to hold “indicative votes” over the prime minister.

“We were told by the chairman of the ’22 committee that they had discussed, I think for some time he said, whether or not they should organise some kind of informal indicative votes. But the executive for the full 22 met and discussed this earlier… and he said they had decided not to organise any indicative votes in his words at this time,” Francois said, adding that he would submit a letter of no confidence anyway.

Andrea Jenkyns, a hardline Tory Eurosceptic, who refused to back May’s deal, did not rule out voting against the prime minister in a no confidence motion, saying it would “take a lot of thinking about”.

Another Tory MP, Marcus Fysh, said: “The cabinet and PM have demonstrated again today that they are on the wrong path. There is a great future ahead but it needs courage and understanding, not fear and vacillation.”

However, one pro-Brexit cabinet source suggested colleagues should hold back their anger for now as they were very sceptical that May could strike a deal with Corbyn.