Senior Labour party figures said it is very unlikely their party would cooperate with the Greens in the future after they adopted a policy treating Zionism as a form of racism.

One Labour minister said they could not foresee how the two parties could work together, while a government official said Labour should formally rule out a future coalition or other arrangement.

There is also pressure within the Liberal Democrats for them to end existing arrangements with Zack Polanski’s party, with some senior Lib Dems calling on the party to end its coalition with the Greens in Southwark, south London.

Green members voted at the party’s conference on Sunday to adopt a binding policy that says Zionism should be treated by the party as racism, and which calls for a single Palestinian state in place of Israel.

After the vote, Bridget Phillipson, the Labour chair, called the move “shameful”, saying it highlighted how vital it had been for her party to tackle antisemitism under the leadership of Jeremy Corbyn.

While Phillipson’s statement was backed by her fellow ministers, there was debate as to whether Labour should go further and formally rule out any ties with the Greens, for example if a future general election delivered a hung parliament.

A source linked to the Jewish labour movement said Labour should “absolutely” rule out governing with the Greens, arguing the policy raised serious questions about whether its treatment of Jewish members could breach equality law.

It follows months of speculation of possible cooperation between the parties. Polanski said earlier this year that the Greens could consider an electoral pact with Labour under Andy Burnham or Angela Rayner, while ruling out one under the former prime minister Keir Starmer.

Labour views the Zionism motion, and the criticism that has followed, as a means to simplify its political argument against the Greens at a time when Polanski’s party has increasingly sought to attract disillusioned Labour voters on the party’s left.

A major test of this will come on Thursday, with voting in the Holborn and St Pancras byelection, where Polanski is seeking to win Starmer’s former seat from Labour.

The Greens have poured huge resources into the contest, with Polanski telling the Guardian that it is “really on a knife-edge”. Despite the Greens’ campaigning efforts, helped by their massively increased membership, Labour are considered the favourites to win.

The Lib Dems and Greens already govern together in Southwark after May’s local elections, with the Greens as the senior partner.

Following the Zionism motion, both Southwark parties released a “joint administration statement against antisemitism”. Without mentioning the new Green policy, it said they would “continue to work with Jewish community organisations to make sure they know they have a place in Southwark”.

It brought a scathing response from some senior Lib Dems. Tagging Victor Chamberlain, the Lib Dem deputy leader of Southwark, Sarah Ludford, a peer and former MEP for the party, wrote on X that she did not understand “how you think this greenwash is an adequate response to the Greens’ antisemitic ‘Zionism is racism’ motion, from which I believe you should entirely distance yourselves”.

Another Lib Dem peer, Lynne Featherstone, who was formerly an MP, replied to a post by Chamberlain to say: “I would ditch them. Grow a pair!”The policy was adopted at the Green party conference in Brighton on Sunday by 1,022 votes to 813, despite being opposed by four of the party’s five MPs.

Polanski, who left the Green conference early on Friday to campaign, stopped short of endorsing or criticising the motion. In a statement on Monday night after the European Greens and German Greens distanced themselves from the policy, Polanski said antisemitism and criticism of the Israeli state “are and must always be completely distinct”. Polanski said he remained proud of the party’s stance on Palestinian rights.