Veteran Conservative MP Bill Cash demanded Rishi Sunak take further action to strengthen his Rwanda legislation in order to stop the boats, warning that the European Union is "in a mess" as a result of illegal migration.
He made the remarks in a House of Commons debate on the Government's legislation.
Cash put forward an amendment to the legislation, aimed at making it harder for individuals to appeal deportations to Rwanda.
He told the Commons: "The EU is in a mess over illegal migration."
More than 11 EU countries have taken action to tackle illegal migration and boost border controls.
Sir Bill Cash warned that the European Union is "in a mess" as a result of illegal migration
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Cash added that "mass immigration is one of the main issues before all nations".
Over 60 MPs have signed amendments aimed at toughening up the Government's legislation.
They will vote on the amendments this evening.
Cash said the rebels "want the Bill to succeed, we want it to work and we want to do what our voters want, but at present it does not."
He added: “Clause two as it stands does not work and that is why I shall put my amendment 10 to a vote, supported as it is by well over 60 Members of Parliament.
“Clause two of the Bill needs to be amended with clear and unambiguous words and with a full notwithstanding formula, not the one that is currently on offer.
“This formula has been used throughout our legislative history for hundreds of years – but most recently it has been enacted in our most important domestic and constitutional legislation without opposition, namely section 38 of the Withdrawal Agreement 2020. The sovereignty of the Crown in Parliament is democracy.”
Tory former cabinet minister Sir Simon Clarke told MPs that "this is our last chance to act in this Parliament".
Meanwhile, former Immigration Minister Robert Jenrick, who has introduced his own amendment to the legislation, asked: "How much are we actually willing to do to stop the boats? How (much) are we willing to take on the vested interests, balance the trade-offs, take the robust steps that will actually work?
“The only countries in the world that have fixed this problem, latterly Australia and Greece, have been willing to take the most robust action, are we? Well, I am.
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“I want to stop the boats and secure our borders. This is a difficult issue, but we’re not a parish council, struggling with some kind of intractable legal issue, we’re a sovereign Parliament, the power is in our hands, we have agency.
“The law is our servant, not our master. I would urge all right honourable and honourable members to support the amendments in my name and those of my honourable friend the member for Stone (Sir William Cash) and create a scheme that actually works.
“That’s what our constituents expect of us, that is the promise that the Prime Minister has made to them and the whole country.”
