Keir Starmer is being urged to clarify his approach to Labour frontbenchers attending trade union picket lines, as leftwing campaigners press the party’s MPs to support striking workers.

Starmer’s allies say he will decide whether to lift the picket line ban when he returns from his holiday on 15 August, after an embarrassing standoff with Lisa Nandy, the shadow levelling up secretary, who was pictured chatting with striking CWU workers in her Wigan constituency on Monday.

Three shadow cabinet members told the Guardian that after the clash with Nandy, Starmer should let the issue drop. “She’s talking to her constituents, who are on a picket line, to find out how they feel,” said one. “There’s a world of difference between that and standing on a picket line with a placard.”

Another said that by issuing a memo urging frontbenchers not to go to picket lines during the recent RMT strike, Starmer’s office had ended up in “the worst of all worlds, judging each strike on its merits and deciding which one they like”.

A third shadow cabinet member said Starmer’s memo, sent before last month’s RMT strike, had been a specific response to the fact that Boris Johnson’s government was seeking to blame Labour for the disruption on the railways. “At that point in time, helping Johnson with that endeavour would have been a bit stupid.”

Several weeks later, they suggested the ongoing row risked detracting from Labour’s policies on tackling the cost of living.

Nandy’s team has insisted she informed Starmer’s office beforehand of her intention to attend the CWU picket in her constituency. But a senior Labour source said it was made clear to her that Starmer did not expect to see pictures of shadow cabinet members on a picket line.

The account of the meeting remains disputed between the two sides. One exasperated party adviser described the handling of the issue by Starmer’s office as “a car crash”, adding that it was “predictable, and predicted”, that with a series of strikes expected over the summer, the picket line ban would lead to ongoing confrontation.

No further action is expected to be taken against Nandy, but the row has stoked tensions in Labour’s top team over the issue.

Two other frontbenchers also visited CWU pickets: the shadow employment minister, Imran Hussain, in Bradford and the Labour whip Navendu Mishra, in Stockport. Both are expected to be spoken to but not sacked.

The Labour deputy leader, Angela Rayner, is understood to be one of those shadow cabinet members who is sceptical about the picket line ban, and has made her concerns known to Starmer – but she has stuck to the agreed position, tweeting her support for striking workers without appearing publicly alongside them.

Rayner and the shadow culture secretary, Lucy Powell, held an online meeting with senior figures from the CWU including its general secretary, Dave Ward, on Monday.

They sent a joint letter to the BT chief executive, Philip Jansen, on Tuesday, urging him to meet workers’ representatives directly, to try to reach a settlement.

The frontbenchers called his decision not to do so “highly unusual and deeply damaging, not just to the company but, given your role in critical national infrastructure, the interests of the country as a whole”.

As the uncertainty over Labour’s stance continued, the leftwing campaign group The World Transformed said it would hold a “festival of resistance” alongside the party’s conference in Liverpool, at which leftwing Labour MPs would speak beside striking workers.

The Liverpool West Derby MP, Ian Byrne, said: “Trade unions have been leading the way in demanding fairness and dignity for working people, and it is crucial that we support them.”

Momentum, the Labour grouping that grew out of Jeremy Corbyn’s leadership campaign, also plans to spend the summer putting pressure on the party to do more to show solidarity with struggling workers.

“As the Tories deliver pay cuts for key workers and energy bills soar, Labour has a huge opportunity to show it is on the side of working people. But right now Keir Starmer is squandering this chance with his farcical picket line ban,” said co-chair Hilary Schan.

“Momentum won’t let workers and trade unions be abandoned. In the coming weeks, we will campaign across the country for Labour MPs to stand with workers on the picket line alongside ordinary members, and to support an inflation-proof pay rise.”

Starmer sacked the shadow transport minister, Sam Tarry, last week after he appeared on a picket line. Starmer’s office insisted that was because he had carried out a series of unauthorised interviews and made up policy on the hoof, including suggesting workers should not be given pay rises that fail to match inflation.