Zack Polanski has urged voters to back the Greens to force changes from Andy Burnham, arguing his party has the power to move Labour in “the right direction”.

In his speech to the party’s annual conference, the Green leader said that “sustained pressure” from his party had made forced Labour into changing its stance on issues including climate and its stance towards Israel.

He told activists in Brighton that Labour had failed to take action on housing, as he called for a three-year cap to limit rent rises in the private sector.

And he said that voting for the Greens would force changes from the government, telling members: “Vote Green, and watch Labour move”.

Polanski arrived in Brighton facing questions over his leadership of the party amid signs the Greens’ rise in popularity last year may have waned, and how he would respond to Labour’s change of leadership under Burnham.

In his half-hour address, he did not mention the Conservatives or Reform UK but launched repeated attacks on Labour’s record in office.

He criticised Labour for making “slogans without action” on the cost of living and vowed only his party would end “Rip Off Britain”.

And he was particularly critical of Labour’s record on housing, where he accused the party of failing to take on the “powerful vested interests of developers and big landlords”.

Instead, he urged the government to enact an “emergency brake” on private rents, under which they would be prevented from rising above the lowest of consumer price index measure of inflation, wage growth or 2%, for three years.

He argued that pressure from the Greens in the face of government “inaction” had forced Burnham into calling an emergency Cobr meeting this summer amid record-breaking hot and dry temperatures.

The Greens, he added would not “hesitate” to tax “extreme wealth”, as he repeated the party’s call for a so-called windfall tax on back profits – an issue where the government has faced pressure from unions.

“Through our sustained pressure – and our historic wins – we have held the worst instincts of the Labour government in check.

“And we have started to move them in the right direction. But we can’t wait for them to get there on their own.”

He also sought to draw a clear dividing line with the government on the issue of oil and gas, ahead of looming decisions for the government on whether to approve the Rosebank oil field and Jackdaw gas field.

Burnham has stuck to Labour’s manifesto commitment not to issue new oil and gas licences, but has left open the possibility of approving the two sites.

This summer’s wildfires, Polanski told the conference hall, should prove the “final nail in the coffin for new oil and gas”.

He began his address by celebrating his party’s surge in membership since his election as party leader a year ago, and electoral successes including the hundreds of councillors it gained in May’s local elections in England.

But his speech did not touch on an issue that could divide the membership over the weekend, ahead of a probable vote on a motion put forward by members that describes Zionism as a form of racism.

The motion defines Zionism as an ideology in support of “an ethnonationalist Jewish state” and seeks to shift the party’s position to supporting a “single democratic Palestinian state in all of historic Palestine”.

The current form of the motion has drawn criticism from senior figures, including deputy leader Rachel Millward, who earlier described it as “problematic”.

Before the conference, Polanski declined to say whether he would support the motion in its current form but said he wanted to see it changed.

He has said he wants to see the motion amended to specify that it should not be used to discipline Jewish members attending synagogues that consider themselves Zionist.

He is also supporting a change that would replace the call for a single Palestinian state with backing for a “lasting settlement granting equal rights for all” to be “shaped and determined by Palestinians themselves”.