The Green party’s only MP, Caroline Lucas, has called on Labour to support multiparty politics by entering into “progressive pacts” with other parties in certain constituencies.

Writing in the Guardian before a televised Labour party leadership hustings on Wednesday night, the MP for Brighton Pavilion said she was relieved to see Jeremy Corbyn on the candidate shortlist as it would ensure that government cuts, Trident and climate change would be debated.

“Whoever takes over the reins of the Labour party needs to recognise that, if Labour is to increase its relevance and appeal, it needs to become a movement that embraces the energy and vibrancy of all those who support a progressive, multiparty politics, both inside political parties and in our communities,” Lucas writes.

“This must include support for a fairer voting system, a commitment to genuine engagement with voters, and an open mind, at least, on locally agreed electoral pacts.”

Lucas suggests Labour, the Greens, the Liberal Democrats, the SNP and Plaid Cymru could give local branches the power to back candidates from other parties, allowing them to set out core pledges that a parliamentary candidate must follow, if they want cross-party support.

The former Greenleader said that many Labour or Lib Dem candidates would never get approved by a Green party branch and vice versa, adding: “But what I cannot be more sure of is the fact that those of us who are serious about addressing the climate crisis, or halting and reversing the destruction of our welfare state, must find a way to work together – and do so quickly.”

At a meeting before the general election last month, the leaders of the SNP, Plaid Cymru and the Green party said they would work together wherever possible to change politics and “battle the Westminster parties’ obsession with austerity”.

On Monday, Corbyn, the MP for Islington North and a key figure on the left of the Labour party, unexpectedly secured – with minutes to spare – the 35 nominations required to stand in the party’s leadership race, which was triggered by the resignation of Ed Miliband after the general election defeat.

Lucas’s comments come as the political theorist Alan Johnson wrote an open letter to Corbyn on the leftwing website Left Foot Forward, saying that while he agreed with the MP on many things, he could not vote for him because of his support of Hamas and Hezbollah.

“You won’t get [my vote] because Labour’s best traditions also include anti-fascism and internationalism while your support – to me, inexplicable and shameful – for the fascistic and antisemitic forces of Hezbollah and Hamas flies in the face of those traditions,” says Johnson.

“I just do not understand how you can support so unthinkingly those political forces which oppose to their dying breath everything – literally, everything – the labour movement has ever stood for: trade union rights, freedom of speech and organisation, women’s equality, gay and lesbian rights, anti-racism, the enlightenment, and reason.”

Labour’s leadership candidates will take part in a one-hour Newsnight special in front of an invited audience in Nuneaton on Wednesday night. Ballot papers will be dispatched on 14 August, voting closes on 10 September and the result will be announced on 12 September at a special conference.

Andy Burnham, the shadow health secretary and current frontrunner, received 68 nominations from MPs, mainly from the north. Shadow home secretary Yvette Cooper received 59, shadow minister for care Liz Kendall 41 and Corbyn 36.