In a letter to the Prime Minister, the former minister urged him to look at cutting ties with the ECHR to prevent Strasbourg judges from meddling in Britain’s illegal immigration crackdown.
It comes after an 11th-hour intervention by the European court grounded the first Rwanda deportation flight last year.
Ms Jenkyns told the Express: “The Prime Minister has a duty to stand up for the people and implement the policies that they believe in.
“The ECHR has already shown a willingness to intervene in our border policy. If we have reason to believe that they will do so again, then the UK must withdraw from it immediately.
“Illegal crossings harm the country as a whole, and harm many of the people involved as well.”
In her letter to the PM hours after he backtracked on his promise, Ms Jenkyns conceded Channel crossings are not a “simple issue to resolve” as there are “many competing factors to take into account”.
But the Brexiteer insisted “we are able to remove one of these factors from the equation entirely”.
She said: “We must not, and cannot, let the British people down on this issue of national importance.
“They deserve a Government that is willing to stand up for what they believe in, and it is only the Conservatives that can deliver on this.
“If this means withdrawing from the ECHR, they I fully support this course of action, and I strongly encourage you to consider this path going forward.”
Tory MP Jonathan Gullis warned the Tories will “suffer the consequences” at the next election, expected in autumn 2024, if they do not get a grip on small boats.
Mr Gullis has spearheaded a series of amendments aimed at toughening up the Illegal Migration Bill, which is going through Parliament, including ignoring rulings by the Strasbourg court.
The Stoke-on-Trent North MP said: “The Prime Minister and the Home Secretary are aware of the amendments that I and other colleagues have been laying to the Illegal Migration Bill, which we believe are vital to making sure that the Prime Minister can deliver on his pledge to stop the boats.
“Because if we do not stop the boats then the British electorate will make us suffer the consequences for it at the ballot box at the next general election.
“One of our amendments is very clear that we wish to ensure that in this particular area controlling of our borders that the European Court of Human Rights has absolutely no jurisdiction to prevent the deportation of illegal economic migrants.
“And I therefore hope that the Prime Minister and the Home Secretary will get behind the work of Danny Kruger, myself and others to ensure we can deliver on this important promise to the British people.”
In an interview with Conservative Home on Thursday, Mr Sunak admitted his plans to curb Channel crossings “won’t happen overnight” and declined to promise they could be completed by the next general election.
The Prime Minister pledged to “stop the boats” as one of his five top priorities.
Asked if he will be able to do that by the next election, he said: “I’ve always said this is not something that is easy. It is a complicated problem where there’s no single, simple solution that will fix it.
“And I’ve also said it won’t happen overnight. I’ve been very clear about that.
“People should know it’s very important to me. It’s hugely important to the country that we need to fix the system as a matter of fairness.
“It’s not fair that people are breaking the rules and coming here illegally.”
Mr Sunak said he expects a legal battle over his Illegal Migration Bill, which would prevent people arriving in the UK illegally from being able to remain in the country.
He added “there may well be” an interim judgment from the ECHR against the policy, as happened with the Rwanda scheme.
The PM said: “That’s always likely to happen in these cases and we will robustly challenge those, as we are doing with the Rwandan cases that are currently working their way through the court system.
“You have to expect legal challenge on these things; our job is to robustly defend them and that’s what we’ll do.”
It comes after figures showed more than 4,500 people have been detected crossing the English Channel in small boats this year despite a promised crackdown.
No 10 has been contacted for comment.