The shadow chancellor has said Labour would back a delay to Brexit to help secure a better withdrawal deal, as the party retreated from supporting a parliamentary vote on a second referendum this week.

John McDonnell said it was no longer the right time to vote on a second referendum on Tuesday, because the priority should be defeating May’s Brexit and then trying to help negotiate a better one.

He had previously said Labour would either put forward an amendment calling for a second referendum or support a backbench one at the time May put her Brexit deal to a vote on 12 March.

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His comments will disappoint some in the party who want Labour to have a clear position in favour of a second referendum as the top priority. Senior figures in the People’s Vote campaign, however, believe there is not yet enough support in parliament for a second referendum. Alastair Campbell said this would only happen when “it becomes clear there is not a majority for any specific form of Brexit”.

McDonnell suggested Labour would back an extension to article 50 to give time to seek a better deal when that option is put to a vote on Thursday. He said the party could help to secure such agreement involving a customs union within weeks, but that article 50 should be extended as long as was necessary to strike a deal.

He said it was still Labour’s policy to support a second referendum, but only if parliament proved unable to agree on a better outcome than May’s withdrawal agreement.

He told the BBC’s The Andrew Marr Show: “We’ve got to abide by exactly what we’ve said at Labour party conference, which is we go through the sequence of respecting the referendum, preventing a reckless deal that Theresa May is bringing forward, preventing a no deal, looking to see how we can construct a deal which we think could protect jobs and the economy, and failing that going for a general election or failing that going back to the people.

Facebook Twitter Pinterest McDonnell called Theresa May’s deal ‘reckless’. Photograph: Chris J Ratcliffe/Getty Images

“And this week, we thought this would be the week in which Theresa May brought back for a meaningful vote a different deal, a new deal. It doesn’t look like that. It looks as though she’s bringing back the same deal, so I think it will have the same result and it’ll be thrown out. And then we’ll move into a situation where we, at least we can try and vote down a no deal, and then I think, yes, further negotiations will take place.

“My view is everything we do this week has got to prevent a no deal and a bad deal. Other discussions will take place but we’ll always, exactly as our party conference said, we’ll always keep on the agenda if necessary. If parliament can’t agree we’ll have to go back to the people. We’ll be forced to.”

His position was echoed by the shadow Brexit secretary, Keir Starmer, who suggested Labour wanted a straightforward vote on May’s deal on Tuesday. “I think across parliament now people know the deal is the same. There is a strong sense that it should be an up-down vote on the deal,” he told Sky’s Sophy Ridge on Sunday.

“Now that is not just a Labour position. Back on 15 January, when we first went through this exercise, there were lots of amendments down and, in the end, across the house, everybody pretty well pulled their amendments and said we need to know the size of the defeat, if it is a defeat, and we are back to that moment on Tuesday.

Facebook Twitter Pinterest Keir Starmer with Jeremy Corbyn. Photograph: Thierry Monasse/Getty Images

“That doesn’t mean that the public vote is gone, it doesn’t mean we won’t come to it … Tuesday is about exposing the weakness of the prime minister and then moving on.”

Starmer suggested Labour would prefer to back an amendment by backbench MPs than tabling its own, because such a strategy would be more likely to attract support across parliament. He also said Labour’s default position ought to be supporting remain if there were a public vote.

Labour wants to throw its weight behind an amendment by Peter Kyle and Phil Wilson, two backbench MPs, which would offer a referendum on any deal achieved by the government versus a remain option.

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The MPs, however, are now not likely to put that amendment to a vote this week given the scale of defeat that May is likely to face on her deal.

Tom Brake, the Liberal Democrat Brexit spokesman, accused Labour of pulling its punches. “Labour’s apparent belated support for a people’s vote needs to be put to the test very soon. If not Tuesday, when? And their commitment must go hand in hand with a three-line whip,” he said.

Scottish Labour’s conference voted earlier on Sunday to support a second referendum on Brexit, reflecting UK Labour policy to “put forward or support an amendment in favour of a public vote, between the option on the one hand of a credible leave deal and on the other hand remain”.