Sir Simon told The Telegraph: "We have a clear choice. Stick with Rishi Sunak, take the inevitable electoral consequences, and give the Left a blank cheque to change Britain as they see fit.
"Or we can change leader, and give our country and party a fighting chance."
He warned a failure to do so would lead the party to an "election massacre".
Earlier this month a devastating national poll predicted the Conservative Party faces scores of losses in the forthcoming general election set to take place this year.
A senior Tory source hit back at the column, telling The Sun: "This is a self-indulgent attempt to undermine the government at a critical moment for the country. He may claim to be helping the party but the only person he is doing any favours for is Sir Keir Starmer."
Damian Green, leader of the large One Nation group of Tory MPs, tweeted: "Simon Clarke is wrong and unwise to try to start another internal fight. Let’s start attacking our opponents, not each other."
More Right-wing Tory MPs may break rank to launch a coup against Mr Sunak.
But it is far from certain that the bulk of Conservative MPs would join such a revolt.
So the move by Sir Simon, no doubt supported by others in the right of the party, may lead to more Tory bloodletting without ousting Mr Sunak.
The PM’s allies, though, will be alert to the risk of any rebellion gaining momentum which could lead to more Centrist MPs joining it.
Eleven Tory MPs voted last week against the Government’s flagship Rwanda plan including Right-wing ex-Home Secretary Suella Braverman.
Former Brexit Secretary Sir David Davis condemned moves against the Prime Minister.
He tweeted: “This is getting silly. The Party and the country are sick and tired of MPs putting their own leadership ambitions ahead of the UK's best interests."
Responding to some of Sir Simon’s criticism of the PM, Lord Goldsmith who quits as an environment minister in Rishi Sunak's government in June last year, said: "He’s obviously right."
Sir Simon, considered an ally of Sunak's predecessor Liz Truss, was not responding to calls on Tuesday evening.
Former Defence Secretary Sir Liam Fox messaged: “This is not the time for self indulgence and tribalism in the party.
"Those who have an agenda to destabilise the government in an election year should understand the consequences. Having been on the front bench for all 13 years in opposition, it is a miserable place. Be warned."
Lord Barwell, a former Croydon MP who was Theresa May’s chief of staff, said: "The unvarnished truth is that Simon Clarke is increasing the chances of him and his colleagues losing their seats.
"The Chief Whip should remove the whip and send a clear message to other Conservative MPs: unite behind the PM or go find some other party to stand for."
The fresh outburst of Tory civil war came as Mr Sunak’s party has hit the low 20s in the polls, trailing Labour by more than 20 points.
It also was just the day after the PM suffered a defeat in the Lords over his Rwanda plan.
Bury North MP James Daly tweeted: "This is absolute nonsense. The Conservative Party must unite behind the Prime Minister to stop the boats, continue levelling up our country and ensure equal opportunity for all.
"Everything else is self indulgence of the highest order."
Labour MPs called for Mr Sunak to trigger a General Election as his party was plunged into another infighting psychodrama.
Jonathan Ashworth tweeted: "This is a failing, divided government incapable of gripping problems facing the country from the cost of living crisis to state of the NHS.
"More proof that after 14 years it’s time for change. Only Labour has a plan to turn the page & get our future back."
Responding to the Tory infighting, senior Liberal Democrat MP Alistair Carmichael tweeted: "Like a box of frogs."