The Conservative party has experienced an early skirmish in the EU referendum battle after the Commons leader, Chris Grayling, was accused by a fellow Tory of “peddling myths” about the EU following his declaration that membership in its current form was “disastrous” for Britain.

Damian Green, the pro-Europe former immigration minister, criticised Grayling after he became the first member of the cabinet to signal publicly that he will join the campaign to leave the EU.

In a carefully worded article for the Daily Telegraph, Grayling said the crisis in the eurozone and the challenge of migration had led to moves to create a “greater political union” in the EU.

The leader of the Commons wrote: “We have reached what I believe is a crucial crossroads for the United Kingdom. The crisis in the eurozone and the migration challenge have led to calls for still more integration and a move towards much greater political union. It is a path that the UK will not and should not follow.”

Green challenged his former ministerial colleague. He told the Today programme on BBC Radio 4 on Thursday: “I think [Chris] is peddling myths about Britain in Europe ... The key myth in Chris’s article is when he says there are calls for still more integration. It is a very explicit and very important part of the prime minister’s renegotiation that Britain won’t be committed to ‘ever closer union’. That is actually a big change in our relationship with the rest of the EU.”

Green, who is a leading member of the Britain Stronger in Europe campaign, questioned how Grayling could say that the EU was disastrous for Britain so soon after hailing the country’s economic successes in the general election campaign.

He told Today: “I am fascinated he says carrying on as we are would be disastrous for Britain. He and I fought an election campaign last year, a successful election campaign, in which we told the British people we were creating more jobs, we’d kept inflation down, we were bringing the deficit down, were creating millions of new apprenticeships. We have done all that as members of the EU. It seems to me a bit odd to say nine months later: ‘Oh it is all disastrous.’”

Grayling signalled to fellow Eurosceptics that he would be a leading figure in the campaign to leave the EU while respecting David Cameron’s instructions to ministers that they must support his EU negotiations until they have been concluded. He praised the prime minister for seeking to renegotiate Britain’s EU membership terms, which were, he said, currently unacceptable.

“I strongly believe that David Cameron is right to seek new terms for our membership before that vote happens,” he said. “I am someone who believes that simply staying in the EU with our current terms of membership unchanged would be disastrous for Britain. That’s why I have always believed that it is imperative that his renegotiation takes place and delivers as much potential change as possible. It is in the interests of all Eurosceptics and of our country. I want Britain to choose between a changed relationship and leaving, and not between the current situation and leaving.”

Grayling also echoed the prime minister’s call for Tories on opposing sides to treat each other with “respect and courtesy” and he moved to ease tensions by saying that the prime minister should not have to resign if he lost the referendum. He wrote: “We need to continue to act as a team, and to debate the Europe issue in a grown-up and mature way. Regardless of our views on the EU, we need to be supportive of the prime minister and the broader work he is doing as the head of this government. The idea that a vote for leave means he has to go is simply wrong – and no more logical than suggesting that a vote to remain would mean all Eurosceptics had to quit.”

The Commons leader is one of four cabinet ministers who are all but guaranteed to campaign for Britain to leave the EU when they take advantage of the prime minister’s decision to lift collective cabinet responsibility once the negotiations have been completed.

The three other cabinet ministers are expected to be Iain Duncan Smith, the work and pensions secretary, Theresa Villiers, the Northern Ireland secretary, and John Whittingdale, the culture secretary. Priti Patel, the employment minister who first made her name in politics as a member of the late James Goldsmith’s Referendum party, will be thinking carefully about which way to jump.

Grayling showed his strength of feeling on the EU when he told the prime minister in a face-to-face meeting last week that he should announce plans to allow ministers to campaign on either side during the referendum. Cameron announced a relaxation of the rules the next day.

Grayling is keen to mark out his territory as a leading opponent of Britain’s EU membership to ensure he can play a significant role in the Vote Leave campaign when cabinet collective responsibility is lifted. He will be nervous that he could be overshadowed by the more senior Duncan Smith, who is planning to keep his powder dry until the EU negotiations have been concluded.

The intervention by Grayling contrasted with a warning by William Hague, the Eurosceptic former foreign secretary, of the dangers of leaving the EU. In an interview with ITV News, he said: “Would it be in our own interests to leave? That makes me worried. If what then happened was the EU became a lot weaker and the UK disintegrated, then what would we have achieved by leaving the EU?

“There is a risk of that. There will be another referendum in Scotland and it would come quicker if we left the EU and Scottish nationalists would say, if you want to stay in the EU in Scotland, the way to do that is leave the United Kingdom.”

Addressing Grayling in parliament on Thursday, the shadow leader of the House of Commons, Chris Bryant, said the minister needed to get a backbone and be honest when expressing his desire for the UK to leave the EU.

Referring to Grayling’s article, Bryant said: “I was hoping for a proper, full-throated, Eurosceptic intellectual argument from the leader of the house, but oh no. It’s the most mealy mouthed, myth-peddling, facing-both-ways piece of pedestrian journalism that has ever come from his pen.”

“He’s pretending he supports the prime minister’s renegotiation strategy when he’s really desperate to burst out of his pink shirt and mount the barricades with the banner of English nationalism.”

He added: “Apparently the business secretary [Sajid Javid] is going to pretend that he’s in favour of leaving the EU so as to bolster the prospects of his favourite candidate for leader, the chancellor. But, Mr Speaker, this really isn’t a game. It’s not about the leadership prospects of one or other Tory minister. It’s about our constituents’ jobs. It’s about our standing as a nation.”