The Metropolitan police are facing a legal challenge over accusations that they failed to fully investigate Boris Johnson’s presence at lawbreaking parties during the Covid lockdown.

The judicial review is being brought by the Good Law Project, which has a history of challenging the government’s decision-making in the courts, and Brian Paddick, a Liberal Democrat peer and former senior police officer.

Johnson is facing a further threat over the Partygate scandal as the privileges committee, chaired by Harriet Harman, has issued a call for evidence of what the prime minister knew about the parties as part of its inquiry into whether he misled parliament.

The Good Law Project, a non-profit campaign group, originally issued proceedings against the Met in January. The force announced soon afterwards that it would investigate.

Johnson was fined only for attending one lockdown gathering in June 2020 – a party in the cabinet room for his birthday, at which Rishi Sunak, the chancellor, was also present.

Johnson was not fined in relation to other gatherings where he is believed to have been present in November and December 2020 and January 2021. However, some civil servants who attended the same gatherings received questionnaires and fines in relation to those gatherings.

The Good Law Project said it was bringing the case because it believed the public had a right to know the truth about the Partygate investigation and why Johnson’s actions in relation to some gatherings did not attract a questionnaire.

Paddick said: “Members of the public will have seen Boris Johnson raising a glass at a party which he apparently hasn’t been questioned about. I thought: if that had been me, I would have been fined. We are determined that the prime minister should be held to the same standard as the rest of us.”

Jo Maugham, the director of the Good Law Project, said: “We need the Met to be transparent about its actions and this challenge is grounded in a single, simple idea: for the law to have any meaning, it must apply equally to us all. The Met must explain their seeming lack of action regarding this matter. We won’t stop until the full story is uncovered.”

A Met spokesperson said: “We are aware an application has been filed and we will respond to that application in due course.”

Meanwhile, the privileges committee announced it was now taking evidence on Johnson’s knowledge of the activities in 10 Downing Street and the Cabinet Office under Covid regulations. At the end of its inquiry it will determine whether the prime minister misled parliament, which is potentially a resigning matter if proven.

The committee said it was seeking any briefing given to, or inquiries made by, Johnson relating to the gatherings, which have previously been investigated by the police and senior civil servant Sue Gray. It said written evidence could be submitted by named witnesses or anonymously by 29 July.

Oral evidence sessions are expected to begin in the autumn. It is not clear whether these will be held in public or private. A former judge, Sir Ernest Ryder, has been appointed as an adviser to the committee.

Separately, Kate Josephs, a former head of the Covid taskforce who received a fine over a leaving do in Downing Street during lockdown, said she was returning to her job as chief executive of Sheffield city council. She had been suspended from the role and was investigated, receiving a written warning for not having disclosed it to her current employer sooner.

In a statement, she said: “I have made mistakes for which I am deeply sorry. I intend to learn from these mistakes and continue to work hard to be the very best chief executive I can be for our city.”