Metropolitan Police said 126 people have been or are set to be issued fines with No.10 confirming Prime Minister Boris Johnson will face no further action.
The end of the investigation means the report by senior civil servant Sue Gray into lockdown gatherings can be published. It is expected to be released next week.
Now two Conservative MPs have urged people to "move forward" amid more pressing issues concerning the cost of living crisis and the ongoing conflict in Ukraine.
Stuart Anderson, MP for Wolverhampton South West, said it had been an issue which had been taken very seriously and acknowledged it had been difficult for a number of people.
But he added: "We just need to move forward now – people have stopped raising it with me for a while now because of more pressing issues, with the cost of living situation and what's happening in Ukraine."
Meanwhile Suzanne Webb, MP for Stourbridge, added: "As far as I’m concerned this matter is now closed and it’s time to move on and for everyone to concentrate on the major issues we all face like the cost of living and the war in Ukraine.
"The amount of time, effort and cost has, in my view, been totally out of proportion to what happened."
The Met Police said detectives have made 126 referrals for fixed penalty notices (FPNs) to the Acro Criminal Records Office relating to events on eight dates, May 20, June 18 and 19, November 13 and December 17 and 18 in 2020 and January 14 and April 16 in 2021.
The recipients of the fines include 53 men and 73 women, with some people receiving more than one fine. Police refused to confirm the identity of any of those involved.