An organisation pushing the Green party to equate Zionism with racism has encouraged people to join the party specifically to support that agenda, and has links to activists who say that pro-Israel “infiltrators” must be rooted out of the UK, the Guardian has learned.

Some Green members are increasingly concerned that the party risks being manipulated by extremist outsiders over a motion to be voted on at the party’s annual conference this weekend, which states that “Zionism is racism”.

Some Jewish members have said privately they fear it will be difficult for them to remain in the party if the policy passes.

Zack Polanski, who leads the Green party in England and Wales, has come under pressure to take a definitive stance on the motion amid worries the controversy will harm the party in next week’s key Holborn and St Pancras byelection, where Polanski is seeking to win Keir Starmer’s former seat.

The motion came top of a members’ ballot of policy issues to be debated at the event in Brighton. It calls for a single Palestinian state and, if passed, it would mean members who support Zionism – the movement for a Jewish state – could be disciplined for racism.

The controversy reflects a longstanding debate about the definition of Zionism, the political movement whose supporters see it as the necessary struggle for a Jewish homeland, and whose critics see it as a colonial project that has inevitably led to the dispossession of Palestinians. The term Zionist is, meanwhile, sometimes used as a synonym for Jew by antisemites.

Efforts to push the policy have been led by Greens for Palestine (GfP), a group not formally affiliated with the party. In repeated social media posts over recent months, GfP has urged backers of the idea to sign up as Green members specifically to get the motion debated at the conference and then adopted.

Polanski last week declared he was anti-Zionist, adding that Zionism was a form of racism because it involved the displacement and genocide of Palestinians. But he has supported amendments to tone down the motion. Lubna Speitan, a leading member of GfP who co-authored the motion, has rejected the amendments.

“It doesn’t matter what the leadership thinks,” Speitan said in a recent video, adding: “We are certainly not here to negotiate the terms of our liberation or oppression with any of our oppressors.”

GfP and Speitan have links to a group called the Anti-Zionist Movement (AZM), a more militant campaign group that argues that the “so-called Jewish state” should be dismantled, along with “Zionist organisations” in the UK and elsewhere.

A key member of AZM is David Miller, a former academic who was sacked by Bristol University over his criticisms of Israel, and subsequently won a tribunal case after it ruled he had been discriminated against because of his anti-Zionist views. He now presents a show for Press TV, the Iranian state channel.

In social media posts, Miller has argued that Zionists have, as “infiltrators and subversives”, gained access to not just all UK political parties but also “the media, entertainment industries, the law, financial institutions, sports and all sorts of apparently obscure parts of the UK”.

GfP and AZM have collaborated on a series of social media posts, and Speitan attended an AZM meeting in London this year. In a video posted by AZM about the meeting, Speitan said it was important for anti-Zionist groups to collaborate.

Speaking in the same video, Miller said his aim was to “dismantle Zionist organisations wherever they are in the world, including the 3,000 or 4,000 Zionist organisations in this country”.

Some senior Greens say they are deeply worried about the links. One said: “I just don’t understand why Zack hasn’t provided any leadership on this, especially when we have such a crucial byelection just days later.”

A spokesperson for the Greens said: “The Green party is a democratic party and membership has grown as more people join to support our full policy platform. The vast majority of members joined prior to a specific attempt at mobilisation.”

They added: “The Green party does not support the views of the AZM.”

A spokesperson for GfP cited Miller’s employment tribunal, saying it “concluded that anti-Zionist beliefs constitute a protected belief”, adding: “We reject all conflations of anti-Zionism with antisemitism, just as we reject the settler colonial project in occupied Palestine.”

Asked about the links to AZM, they added: “We welcome the adoption of our motion by all anti-racist organisations, political parties and unions.”

GfP, the statement added, “affirms the Palestinian people’s inalienable right to self-determination, including the right of the Palestinian people to resistance and liberation from Israeli occupation, domination and subjugation” via any means under international law.