The Conservative MP for Penrith and the Borders has released a statement saying he is "shocked and appalled" at partygate.
He also called for a leadership election once the Ukraine and Russia conflict comes to an end.
Boris Johnson and Rishi Sunak were both fined for breaking lockdown rules for attending the PM's birthday party.
However, it is thought the PM could be facing more fines as well.
Dr Neil Hudson said: "As I have previously said, I was shocked and appalled at the reports of numerous gatherings and parties at Downing Street.
"For me, this is a matter of integrity and honesty at the heart of Government and we need to get clarity and closure as soon as possible.
"I maintain my position that I categorically will not defend the indefensible.
"I fully share the country’s outrage and upset about these Downing Street parties when people up and down the land were making huge personal and sometimes tragic sacrifices to do the right thing and obey the public health rules.
"Again I maintain, if rules and indeed the law have been broken, then quite rightly there should be serious consequences for all those involved, no matter who they are."
He then goes on to say that it was the "law makers" that broke their own law.
He added: "The fact that the Prime Minister and Chancellor have been found in breach of the Covid rules and issued with Fixed Penalty Notices is extremely disappointing.
"The fact that the law makers went on to break those very laws they brought in to keep us all safe is deeply damaging for our democracy.
"That situation is untenable moving forward. That said, I do not believe it would be prudent or responsible to change the leadership of the Government in the midst of the international crisis that is the war in Ukraine.
"Destabilising the UK Government would undermine international efforts to support the Ukrainian people and bring the despicable Russian invasion to an end.
"I will therefore be looking to the Prime Minister to show the statesmanship he has been showing with Ukraine, and outline a timetable and process for an orderly transition to a leadership election as soon as the international situation permits."