Labour’s four-month leadership election to replace Jeremy Corbyn has hampered the party’s response to the coronavirus pandemic, according to some of its MPs.

Critics said the party’s leadership has been sluggish in responding to the crisis and Corbyn, as outgoing leader, has failed to command authority.

They said that it had instead fallen to backbenchers and shadow ministers to put pressure on the government, and called for the leadership race to be wrapped up early.

Lucy Powell MP, who is leading an inquiry into Labour’s general election loss, said she sympathised with Corbyn, who was facing an unprecedented international crisis as leader of the opposition, but that he could have ended the contest sooner. Keir Starmer, Rebecca Long-Bailey and Lisa Nandy have been battling for more than 11 weeks to succeed him. Voting is due to end on 2 April.

She said: “We could have easily brought forward the election of the new leader. We are now in the worst of all worlds. Despite their best efforts, Jeremy Corbyn and John McDonnell feel less relevant.”

The Manchester Central MP said the party needed “that sense of clarity on leadership rather than different messages coming out from different quarters”.

She urged the party to act, saying it was not too late to bring forward the election date so the next leader could take over and start attending key government meetings on coronavirus, such as the privy council.

Chris Matheson MP, a shadow cabinet minister backing Starmer, said: “The lesson for the future is seriously that such a protracted contest does nobody any good.”

Labour’s national executive committee (NEC) fixed the timetable for the leadership election in January amid criticism that it was deliberately long to help Long-Bailey, the shadow business secretary, a close ally of Corbyn.

The party has said it is reluctant to bring forward the election as it would risk disenfranchising members and supporters who haven’t yet voted.

One backbencher said Corbyn should have immediately stepped down and an acting leader would have galvanised key players from the parliamentary Labour party on coronavirus, rather than seeing a piecemeal approach, which has included amendments to the emergency legislation from MPs Harriet Harman and Chris Bryant and shadow health secretary Jonathan Ashworth, who personally pushed for enforced physical distancing.

They said: “Fundamentally, it goes back to the fact that Jeremy stayed in post after the general election, which led to a ridiculously long leadership election. A sensible acting leader would never have allowed the NEC to allow it to go on for so long. We would have had a leader standing at the dispatch box with real credibility.”

The MP suggested Labour could have had more influence by creating a shadow Cobra, the government’s emergency committee. “Or you could have credibly asked the government to set up a cross-party taskforce using Labour’s expertise on DWP issues.”

A Labour party spokesperson said: “Jeremy and the shadow cabinet have led a strong and effective response to the coronavirus crisis, offering constructive support to the government where possible and pushing it whenever necessary on key issues such as protection and testing for NHS staff, help for renters, income protection for workers, the self employed and those on insecure contracts, increasing statutory sick pay, and most recently calling for enforcing social protection measures.

“In a number of key areas, the government has followed Labour’s demands for action.”

Labour said that Corbyn wrote to the Boris Johnson on 14 March calling for mortgage and rent holidays, both of which the government has since adopted, and an expansion of statutory sick pay.

A shadow frontbencher also criticised the core Labour leadership for taking too long to decide whether to support a lockdown.

“Jeremy has been really cautious,” they said. “People are looking for politicians for leadership. They’re not seeing it in government and it’s lacking on our side as well.

“The Labour leadership is just as guilty as Boris Johnson for not taking it seriously as they should. It feels like Jeremy and John were both completely absent until last week.”

It is understood that Shami Chakrabarti, the shadow attorney general and former director of civil liberties organisation Liberty, surprised fellow shadow cabinet members when she stepped in to encourage the shadow home secretary, Diane Abbott, that proportionate legislation could work, if it included a sunset clause.

Corbyn’s decision to continue attending the Commons, and carrying out an interview on Sky’s Sophy Ridge on Sunday, despite the government guidance that people over 70, regardless of any medical conditions, should consider physical distancing has also angered colleagues. “That was just wrong. He should lead by example,” said the frontbencher.

But a Labour source said: “Using a time of national crisis to get in a last dig at Jeremy is divisive, silly and about as low as you can go. They should be ashamed of themselves.”