Conservative MP Daniel Kawczynski has voiced support for the Government plan, which was revealed by Deputy Prime Minister Dominic Raab.
The move comes after the Government's much-criticised plan to send asylum seekers to Rwanda has faced numerous legal challenges.
Its most recent effort to fly asylum seekers to the country was cancelled after a European Court of Human Rights (EHCR) ruling which blocked the plan – despite it being approved by UK courts.
Mr Raab was proposing legislation on Wednesday in response. He said it would assert that British courts do not always need to follow case law from Strasbourg and that the Supreme Court in London is the ultimate decision maker on human rights issues.
It would also mean that interim measures such as the one issued by the EHCR over the Rwanda policy are not binding on UK courts.
The plans have been criticised by Amnesty and the Labour Party.
Mr Kawczynski however said he wanted action taken after the EHCR "thwarted the will of the British people".
He added that the move had "impeded the British people’s desire to start regaining control of our borders".
"Having received the most votes in the 2019 General Election, the Conservative Party, myself included, stood on a manifesto that promised to control Britain’s borders," said Mr Kawczynski.
"This commitment clearly meant establishing control over who can enter and who can leave our country. The ECHR’s involvement has however undermined the Government’s intention to carry out the desires of the British people."
He added: "After the first flight had been grounded, I stood up in the House of Commons Chamber and urged the Home Secretary to consider withdrawing Britain’s membership from the ECHR.
"Unsurprisingly, I was met with boos and groans from the opposition benches, which are made up of members whose disapproval was in direct conflict with how people feel towards illegal migration.
"Our current Human Rights Act which enshrines the ECHR in British law, introduced under Tony Blair’s first administration, is no longer fit for purpose.
"The Government now needs to pave the way for new legislation that will restrict the use of Article 8 and define a British Bill of Rights, thereby restricting the ability of ECHR judges to impede the Government’s efforts to deport illegal migrants.
"This catastrophic situation of failing to resolve the crisis across the English Channel cannot continue."
Sacha Deshmukh, Amnesty International UK's chief executive, has criticised the plans, saying the legislation would represent "a giant leap backwards for the rights of ordinary people".
"Ripping up the Human Rights Act means the public is being stripped of its most powerful tool to challenge wrongdoing by the Government and other public bodies. This is not about tinkering with rights, it's about removing them," he said.
Shadow Justice Secretary Steve Reed has also warned against the move, saying: "Labour is proud that the Human Rights Act has allowed millions access to justice, protect victims of crime, and ensure our loved ones get the care they need.
"But this Conservative 'Bill of Rights' con will take those rights away, preventing people with health problems from objecting to 'do not resuscitate' orders being placed on them in hospital without their consent, block women from forcing the police to investigate cases of rape, and will stop victims of terrorist atrocities and major disasters like Hillsborough from seeking justice."