Theresa May was accused last night by a former cabinet colleague of planning the “biggest giveaway of sovereignty in modern times”, as she faced a potentially devastating pincer movement from Tory remainers and leavers condemning her Brexit plans.

The day after Jo Johnson, the pro-remain brother of former foreign secretary Boris Johnson, resigned from the government and called for a second referendum on Brexit, former education secretary Justine Greening launched an attack on the prime minister, saying her plans would leave the country in the “worst of all worlds”.

Piling yet more pressure on May, Greening – who resigned from the cabinet in January – backed the former transport minister’s call for another public vote and said MPs should reject the prime minister’s deal. Greening told the Observer: “The parliamentary deadlock has been clear for some time. It’s crucial now for parliament to vote down this plan, because it is the biggest giveaway of sovereignty in modern times.

“Instead, the government and parliament must recognise we should give people a final say on Brexit. Only they can break the deadlock and choose from the practical options for Britain’s future now on the table.”

Greening added: “Like many of us, Jo Johnson is a pragmatist on Britain’s relationship with the EU. But Conservative MPs can increasingly see that this sovereignty giveaway from No 10 leaves our country with less say over rules that govern our lives … That is not in the national interest, it’s the worst of all worlds and it resolves nothing.”

Her intervention – just days before May hopes to win agreement for her plans in her deeply divided cabinet – shows how Tories on both sides of the Brexit divide are finding common cause, protesting that her blueprint would leave the UK tied to the EU’s economic systems but with no say over the rules that govern them. As a result, they say that rather than seizing back control from Brussels, it would do the reverse and leave the UK with less power.

A letter to the prime minister, organised by the StandUp4Brexit campaign and circulated among Tory party constituency chairs, seen by the Observer, states that May’s proposals represent a “significant blow to our sovereignty”.

It says that an agreement that would leave Britain “trapped in a customs union with the EU indefinitely”, as current plans could do, would “fly in the face of the referendum result” and risk “delivering a Corbyn government at the next election”.

The letter goes on: “As Conservative chairmen, we therefore call on you … to ensure that the final deal complies with those red lines that you set out in both the 2017 election manifesto and your Lancaster House speech – namely leaving the customs union, the single market and ECJ over-all.”

In his resignation statement on Friday, Jo Johnson said the country was “on the brink of the greatest crisis” since the second world war and argued that the Brexit deal on offer wasn’t “anything like what was promised”. He denounced the choice between May’s plans or a no-deal outcome as a “failure of British statecraft on a scale unseen since the Suez crisis” that had left Britain facing “vassalage” or “chaos”.

On Saturday, speaking on BBC Radio 4’s Today programme, he went further, saying another referendum would be the first opportunity for voters to have a say on what Brexit would actually mean, after two years of tortuous negotiations. “My view is that this is so different from what was billed that it would be an absolute travesty if we do not go back to the people and ask them if they actually do want to exit the EU on this extraordinarily hopeless basis,” he said.

Jo Johnson said other ministers who shared his views should also quit. Photograph: Henry Nicholls/Reuters

Asked whether he believed other ministers should quit over the issue, he encouraged them to do so if they shared his views. “I think this is so important that it’s up to MPs to take a stand. I’ve done so, if others feel that it’s right for them to do so, good on them.”

One Tory donor warned last night that May was now heading towards an “explosion” with her own party. “She made incompatible promises to different constituencies,” he said. “An explosion is now the best forecast.”

Campaigners for a second referendum claim that support for another vote is growing. The pro-remain Best for Britain group said that, for the first time, a poll showed a majority of leave voters now backed a second vote. The Populus poll of more than 8,000 people found 52% of those that voted leave now support a final say on the Brexit deal.

Meanwhile, Labour leader Jeremy Corbyn has come under pressure from some of his own MPs for saying that “we can’t stop” Brexit, just two months after he insisted “all options are on the table”, and shadow Brexit secretary Keir Starmer said a second referendum with the option to remain in the EU should be kept open. Many Labour MPs say that if Corbyn were to back a second referendum, there would now be a majority in parliament to hold one.

In an interview with Der Spiegel published on Friday, Corbyn said it was necessary to “recognise the reasons why people voted leave”. Luciana Berger, Mike Gapes, Wes Streeting and Chuka Umunna were among the Labour MPs to criticise the remarks, as a major row brews within the party over whether it should back a second poll if May’s deal were voted down in parliament. Asked on Saturday whether he agreed with Johnson’s call for a second referendum, Corbyn reiterated his opposition: “Not really, no,” he said. “The referendum took place. The issue now has to be how we bring people together.”