Helen Morgan, Liberal Democrat MP for North Shropshire, emerged victorious in a by-election last month where the campaign was dominated by allegations of rule-breaking at Number 10 Downing Street.
The latest revelations centre on an e-mail, alleged to have come from Martin Reynolds, principal private secretary to the Prime Minister, inviting 100 members of staff for drinks in the garden at Downing Street in May 2020.
Mr Reynolds said they should "make the most of the lovely weather", despite England being under tough coronavirus restrictions banning groups from meeting socially outdoors.
Mrs Morgan said that, if true, the latest allegations were more evidence of a 'one rule for us, no rules for them' attitude.
She said: "If it is true it is a real insult to all the people who kept to the rules and obeyed the restrictions at the time.
"If I think about Shropshire in May 2020, the roads were quiet, people were sticking to the rules and it is an insult to them and all the people who tried to act in the interests of public health in the county that people at the top were disregarding that.
She added: "It is extremely frustrating. This would not just be a lack of leadership it would be breaking the law and if it turns out to be true it is incredibly serious.
"It goes back to this one rule for us and no rules for them, it appears to be a pattern of behaviour where the rules were brushed aside.
"If this latest claim is correct people will rightly be angry."
Mrs Morgan said that her own election, where she caused political shockwaves by overturning a 23,000 Conservative majority, had come as people expressed anger at the perceived inequality in the way lockdown rules were followed.
She said: "Voters in the North Shropshire by-election demonstrated very clearly that they were sick and tired of 'one rule for us and no rule for them' and while these revelations keep coming it is time for the government to take a good hard look at the level of leadership they have provided."
Several Conservative MPs have said that they will wait for the outcome of an inquiry being carried out by Sue Gray, a senior civil servant, into the numerous allegations of rule-breaking events being held in Downing Street during the coronavirus pandemic.
Shrewsbury & Atcham MP, Daniel Kawczynski, said: "Sue Gray is investigating, she is highly respected and it would be premature to prejudge her findings before she reports. I am sure she will do a thorough job in investigating these claims.
Craig Williams, Tory MP for Montgomeryshire, said that he would be waiting to consider the findings of the inquiry.
He said: "There is an ongoing investigation being carried out by Sue Gray, her integrity is completely above reproach, her report will be a full and frank assessment and that is what I am waiting to read."
He added: "There is no doubt this government could do better but let's wait for the outcome of the investigation."
Ludlow Conservative MP, Philip Dunne, who spent 17 months shielding from the start of the pandemic, said the allegations would need to be looked at by the investigation – and that if wrongdoing is proved then consequences must follow.
He said: "This is a very serious allegation and it need to be included in the review being undertaken by Sue Gray and whatever she finds, if there is evidence that the allegations are proven then consequences must follow."
Conservatives Lucy Allan, the MP for Telford and Mark Pritchard, the MP for Wrekin, have both been contacted for comment.