Labour’s Brexit policy is now the single biggest barrier to Britain remaining in the EU single market, the Ilford North MP, Wes Streeting, will claim on Saturday.

Streeting is one of a well-coordinated group of vocal backbench rebels campaigning for leader Jeremy Corbyn to harden Labour policy by saying he would back continued membership of the single market and the customs union.

In a speech to the Fabian Society’s annual conference in London on Saturday, Streeting will say: “On the UK’s future relationship with the European Union – the single biggest issue facing our country in a generation – we find ourselves in the terrible position where it is the Labour party that currently stands as the single biggest barrier to the UK’s membership of the single market and customs union.

“With Labour, there would be a majority in the Commons for single market membership, but not without us. If the Labour party announced tomorrow that we would keep Britain in the single market and customs union, it would be a game-changing moment in British politics. The policy would command a majority in the Commons and a majority in the country.”

An amendment to the European withdrawal bill tabled last month by Nottingham East MP Chris Leslie, which he said would ensure the government made legal provision to remain in the customs union, won the backing of more than 60 Labour MPs, against the advice of whips.

Labour’s formal position is that Britain’s interests would be best served by retaining membership of the single market and customs union during the transition period that will begin in 2019.

But it has not yet given details about what deal it would be willing to accept once that period – expected to be around two years – expired.

The shadow Brexit secretary, Keir Starmer, has said permanent membership of a customs union with the EU27 could be a “viable” longterm option and should be kept on the table.

The party’s formal policy is to pursue a “jobs-first Brexit” – and try to appeal to leave and remain supporters. Streeting will say: “The fudge that got us through the general election won’t get us through 2018.”