The Metropolitan Police has announced it is investigating several events in Whitehall and Downing Street for potential breaches of Covid rules.
The Met has not given specific details but the investigation could include the party CEO Kate Josephs attended at the Cabinet Office on December 17, 2020.
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Sheffield Council Leader Terry Fox has confirmed the authority is now taking legal advice.
Ms Josephs was working as director general of the Covid Taskforce and held leaving drinks before starting her new role at Sheffield Council.
She released a statement and apologised just minutes before a national newspaper published the story.
It came after she had repeatedly denied to local journalists that she had been involved in any Downing Street parties.
Her statement said she had gathered with colleagues that were at work that day but it was later revealed an email was sent to 40 guests.
Ms Josephs is currently on paid leave from her £190,000 job but Lord Paul Scriven said she should now be suspended.
He said: "We now potentially have a criminal investigation about this Cabinet Office party. Anybody else lower down in the council who had a serious allegation made about their behaviour and a possible police investigation would be suspended.
"What makes the CEO so important that she doesn't abide by the normal employment rules? Suspending her would send a clear message that the council is taking this with the seriousness that Sheffield expects."
A cross-party committee was set up to look at whether any future action should be taken against Ms Josephs.
It is due to meet again on Thursday and will now be given legal advice on what the options are regarding Ms Josephs.
The committee, which has already met once, was due to report back after the investigation by senior civil servant Sue Gray.
She was looking into alleged Covid rule breaking in Downing Street, government departments and ‘credible allegations relating to other gatherings’.
Her report has been delayed pending the Met Police investigation.