One of Jeremy Corbyn’s key allies has made a bold suggestion that Labour could form progressive alliances or electoral pacts with other parties across the left including the Greens, Liberal Democrats and SNP.

Clive Lewis, the shadow defence secretary, raised the suggestion of an alliance with Caroline Lucas of the Greens in an article for the Guardian, arguing that grouping together with others on the left is necessary and would lead to better decisions.

“Such progressive alliances are now essential not just because that is the only way we can beat the Tories but because that is the way we will make better decisions and take more of the country with us,” he said.

“Frankly, I want to be in government with Caroline Lucas, not against her – and certainly not in permanent opposition.”

He later told the Guardian that this could extend to other parties on the left including the SNP and Lib Dems.

“I sit and listen to Caroline Lucas and seven or eight times out of 10, I listen and think: not sure about that bit but most of it I agree with. When the Tories jeer her, I want to stand up. Half the time when the SNP are speaking, I listen to what Mhairi Black or others are saying and think I agree with that. I listen to Tom Brake [a Lib Dem] and think I agree with what he says on that issue.

“There is a common set of themes and values and principles that we need to identify as progressives and then start to work out how can we work together not just to stop the Tories but to have better politics ...

“The first thing is we are going to have to work within the current electoral system. One of the agreements would have to be all of the political parties except the Tories and a chunk of our own.

Corbyn, John McDonnell and Lucas together at the junior doctors’ march in April. Photograph: Guy Bell/Rex/Shutterstock

“I would probably be being over-optimistic if I thought the SNP weren’t going to play hard and fast but nonetheless they could come under pressure if there was serious talk of some form of electoral pact to stop the Tories, to look at how if there were seats – one where the Liberals have the best chance of beating the Tories, the Liberals go forward, if there is a seat where the Greens have a better chance of beating the Tories, the Greens go forward. If there area seats where a Green candidate standing down would make the difference to Labour, there are ways you can do it.”

His comments immediately annoyed some Labour MPs who said they had fought hard against Green candidates in local elections, including Lucas’s seat of Brighton.

Ian Austin, an opponent of Corbyn and MP for Dudley North, said: “Labour plus greens plus non-voters is still a mathematically impossible, self-indulgent fantasy.”

Phil Wilson, MP for Sedgfield, tweeted: “The cat’s out of the bag, Corbyn’s people want 2 b in government with the Greens. Will this madness plse stop.”

Lewis said he knew some would be upset about the idea but people “have to start thinking about the bigger picture”.

“It’s about beating the Tories but it’s also about better politics because the more people you can bring along, the less tribal you are and better decisions you will make. The more consensus you have the longer term the decisions you make,” he said. “I do believe in a progressive majority and the figures speak for themselves.”

At the last election, the combined vote of Labour on 30.4% and the Greens on 3.8% of the vote was 34.2% – just two percentage points behind the Conservatives on 36.9%. Lucas was the only Green MP elected, after Labour saw off threats in places such as Lewis’s own seat of Norwich South.

Lewis’s article set out the reasons he is backing Corbyn for Labour leader but also set some key tests that the party must pass if he wins the contest as expected.

“Let me be clear: Corbyn is the best candidate because, in his own way, he understands some of the economic and moral challenges we face, and is the product of a deep desire for something new,” he wrote.

“But let me also be clear that electing Corbyn, in and of itself, is necessary but far from sufficient. As well as again electing him, a whole set of other meaningful relationships and ideas need to be put in place.”

He said the parliamentary party must build relationships across all wings of the party and across activists in all elements of civil society.

“Ultimately, though, we have to be honest with ourselves. Corbyn’s leadership has struggled,” he said. “There are good reasons for this, not least the almost permanent attack from the media and sections of the PLP, which have been destabilising from day one.

“But we must also acknowledge that the leadership of the party has not been good enough yet. That is Corbyn’s fault, just as much as it is mine and my colleagues’. Alliances have not yet been built; big ideas have not yet been developed.”