Two Labour MPs campaigning for a second EU referendum have said they have no choice but to work with the Liberal Democrats and other politicians openly critical of Jeremy Corbyn’s policy on Brexit in the hope of eventually securing a vote.

David Lammy and Bridget Phillipson defended their approach at an event organised by the People’s Vote campaign, where they shared a platform with the Lib Dem deputy leader, Jo Swinson, who accused Corbyn of showing a lack of leadership on Brexit.

Phillipson, the MP for Houghton and Sunderland South, said she “disagreed with a lot of what Jo says” but that securing a second referendum “will involve working with people I disagree with on other issues”.

Lammy, the MP for Tottenham, said: “This is an issue that requires courage. You simply cannot please all of the people all of the time. It’s also not a party political issue; the issue of Brexit was never purely party political, there isn’t a Conservative or Labour plan, there is a field of opinion across the party political divide.”

The two Labour MPs were speaking alongside Swinson and the Green party’s Westminster leader, Caroline Lucas, at the launch of a pamphlet criticising Labour’s principal Brexit plan as well as the no-deal and “Norway plus” alternatives.

Swinson opened the event with an attack on Labour’s Brexit strategy, arguing: “We have not been well served by our official opposition.” She accused Corbyn of showing a lack of leadership and Labour’s high command of “ignoring its own members, its conference motion, its own voters [and] the best interests of the country.”

Labour’s leadership had been resisting embracing the idea of a second referendum, having first tried to secure a general election to resolve the Brexit impasse. But pressure has been growing within the party since last Wednesday when Labour lost a vote of no confidence in Theresa May’s government.

On Monday night the party tabled an amendment calling on MPs to have a chance to vote on the option of a second referendum and on its own Brexit alternative, involving staying in a customs union with the EU and what it calls a close relationship with the single market.

Phillipson said the Labour leadership amendment was a step in the right direction and “part of the process that will get us to the point where we can support a second referendum”.

But Swinson complained that Labour had taken only “a baby step forward; I’m concerned about the timescale, with 66 days to go until Brexit. I know that David and Bridget are working hard within Labour to get to a second referendum.”

Labour’s Brexit amendment will be considered next Tuesday as one of several amendments proposing next steps for Brexit. The Labour MPs present at the event said they thought it was right that any vote on whether to hold a second referendum should be held on another date, after Tuesday’s vote.

Phillipson said she wanted the Commons to vote on a second referendum only when it had a chance of succeeding. “I want to make sure when we get to the point when we want to secure a referendum, it is a time when we have the greatest prospects of success.”

Other MPs such as the Conservative Sarah Wollaston have suggested putting down an amendment that would require the Commons to vote on holding a second referendum next Tuesday. Labour’s amendment, if it is carried, would only commit MPs to holding a vote at a future date.