A series of amendments have been tabled by Conservative MPs from the right of the party to beef up the Bill, which returns to the Commons for two days of debates for its committee stage today.
A source told the Times: “She wants to use it to spook us to offer concessions to get them to drop their amendments because a big rebellion would be embarrassing.
“She has basically become a sock puppet for the right.”
But a source close to the Home Secretary denies the claims and branded them “scurrilous rumours”.
The source said: “This is totally untrue and neglects to mention the fact the home secretary has been calling MPs to ask them to give the government time to consider their concerns and not rebel against the bill.
“The people spreading scurrilous rumours like this about the Home Secretary should reconsider and refrain.”
It is understood the potential revolt has now been put on hold as rebels meet ministers to look at how to tighten up the Bill.
As of yesterday, close to 30 Tories had put their name to an amendment to the Bill that would stop the European Court of Human Rights (ECHR) from preventing removals from taking place.
It comes after the ECHR last year granted an injunction, via its Rule 39, that effectively grounded the first flight sending asylum seekers on a one-way ticket from the UK to Rwanda.
In an amendment sponsored by Tory Devizes MP Danny Kruger, he wants the provisions in the Bill to “operate notwithstanding any orders of the Strasbourg court or any other international body”.
Mr Sunak and Ms Braverman have both stressed that they think the legislation complies with international obligations and that Britain would not need to exit the European Convention on Human Rights to introduce the plans.
But in a letter to MPs following publication of the Bill earlier this month, the Home Secretary conceded there is a “more (than) 50 percent chance” the Bill may not be compatible with the convention.
There is also a separate rebellion by those on the liberal wing of the Conservative Party who want a commitment to establishing safe routes via which asylum seekers can come to Britain.
Tory MP Tim Loughton has proposed an amendment that would force the Home Secretary to declare “safe and legal routes by which asylum seekers can enter” the UK.
Asked about the looming rebellion this morning, minister Chris Philp told Sky News: “I think this Bill is very important. I think the public expects the small boats to be stopped.
“One of the Prime Minister’s five priorities is to stop the boats and this Bill is designed to deliver that.
“I don’t think anyone could doubt the Prime Minister’s or the Home Secretary’s commitment.
“As I understand it she is discussing these various amendments with MPs. I’m sure she’s in listening mode as always.
“But this is a well-constructed Bill designed to stop the boats which the public expects the Government to do.”