David Jones MP, the deputy-chairman of the eurosceptic European Research Group (ERG) has predicted any amendments peers make will be swiftly overturned when the legislation returns to the House of Commons. And Robert Oulds, director of the pro-Brexit Bruges Group, warned it was no surprise the unelected chamber is "siding with the undemocratic EU". The Bill is undergoing detailed line-by-line scrutiny in the House of Lords and is currently scheduled for four days of consideration at committee stage.
Cross-party amendments have been tabled to strike out clauses linked to the most contentious part of the Bill, which aim to give ministers the power to breach the Brexit divorce deal - known as the Withdrawal Agreement - brokered with Brussels last year.
The amendments are in the name of Lord Judge, a former lord chief justice, shadow attorney-general Lord Falconer of Thoroton and former Conservative former Lord Howard of Lympne.
Mr Kawczynski, MP for Shrewsbury and Atcham, told Express.co.uk: "This is yet another example where many of us believe if their lordships do implement what they are threatening to do, there is no doubt in my mind that the campaign to abolish the House of Lords will gain even more momentum.
Former Tory leader Lord Howard and Prime Minister Boris Johnson
ERG deputy chairman David Jones MP
"The fact that these unelected people can seek to overturn the common will of the democratically elected lower house shows the huge anachronism of our current constitutional make-up.
"If you are going to overturn the will of a democratically elected chamber then you must be elected yourself.
"I would much rather have an elected senate of 100 senators - I've said this for many years. We don't need 900 elected peers who only need to turn up for five minutes to bank their £350 daily pay.
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Daniel Kawczynski MP said the move made abolition more likely
"I am horrified at the likes of Lord Howard. He was absolutely at the forefront of propagating discipline when he was party leader.
"And now he is no longer the leader of the party, he is seeking to undermine the collective will of over 99 percent of the Parliamentary party."
Mr Jones said: "The elected House of Commons has already voted to pass this essential legislation.
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Robert Oulds said the Lords was "sailing close to the wind"
"There have many occasions when domestic legislation does not reflect treaty provisions.
"Germany, among other countries, has asserted its sovereign right to deviate from international obligations.
"The Lords should respect the will of the people and the will of the Commons.
"I have no doubt that any amendments that pass will be rejected when they return to the Commons."
Mr Oulds said: "The House of Lords is sailing close to the wind if they amend the Internal Market Bill.
"It is no surprise that the unelected House is siding with the undemocratic EU.
"The Lords are putting the sovereignty and integrity of the UK at risk."
Liberal Democrat Lords leader Lord Newby and the Bishop of Leeds, the Rt Rev Nick Baines, are also among supporters of some of the cross-party proposals.
Former PM Theresa May has been critical of the Internal Market Bill
Labour has suggested peers could follow the unusual step of holding votes at committee stage next week to remove these sections of the Bill rather than waiting for report stage, the part of the process where they usually vote on matters connected to legislation.
The Government says powers to override the aspect of the Withdrawal Agreement known as the Northern Ireland protocol are necessary to protect the integrity of the UK.
However, critics argue the powers are not necessary, with Boris Johnson's predecessor as Prime Minister minister Theresa May previously stating an arbitration process to resolve issues would be available - claiming the Government's additions have "no place in this Bill".
If the Lords goes ahead and removes the controversial sections, the Government would then have to try to reintroduce them in the Commons - if they judge they are still required given the state of Brexit talks.