Theresa May has insisted the UK stood its ground in negotiations with the EU after critics claimed her draft deal was heavily weighted in the bloc's favour.
Defending her much-maligned deal on Nick Ferrari's LBC show, the prime minister said the EU had "given in on" several key points, including the Irish border and the European Court of Justice.
"A lot of people look at this and think the UK is the only side that's given anything, that's not the case," she said.
She continued: "There are other areas too where the European Union has felt that a particular approach is right, and we've said 'no', we've held out, we've held our ground and they've given in to us.
"But it's a negotiation. And any negotiation, complex as it is, is actually a negotiation that leads to compromises."
Mrs May refused to be drawn on whether she had offered Michael Gove the job of Brexit Secretary after Dominic Raab stepped down from the role on Thursday.
After much speculation that the Environment Secretary would join the growing number of MPs to resign in protest at Mrs May's deal, Mr Gove has decided to stay on in his current role after reportedly turning down the prime minister's offer.
As he left the Defra office on Friday morning, Mr Gove said he "absolutely" had confidence in the prime minister.
He added: "I am looking forward to continuing to work with all colleagues in Government and in Parliament to get the best future for Britain."
International Trade Secretary Liam Fox was also staying loyal to the prime minister and called for discontented MPs to re-consider their stance.
Speaking at an event in Bristol, he said: "Ultimately I hope that across Parliament we'll recognise that a deal is better than no deal.
"Businesses do require certainty and confidence as they go forward for their planning and there are those around the world who are waiting to get certainty also to begin to discuss trade agreements with the UK. It is in our national interest."
Video report by ITV News Political Editor Robert Peston
Asked whether MPs would be allowed a free vote - that is one in which MPs are not under pressure to vote along party lines - when the Brexit deal comes before Parliament, Mrs May said: "There is Cabinet collective responsibility in this country. Government policy is Government policy.
"There is Cabinet responsibility. The Government will put its policy to the House of Commons."
During the show, where she took several calls from listeners, she repeated her determination to "see it through" following a turbulent day in Westminster on Thursday which saw a string of high-profile resignations including Mr Raab and Work and Pensions Secretary Esther McVey.
A number of junior ministers, including Suella Braverman, Rehman Chishti, Shailesh Vara, Anne-Marie Trevelyan and Ranil Jayawardena, all quit over the deal too.
Speaking at a press conference in Downing Street on Thursday evening she said she believed with "every fibre of my being that it is the right one for the country".
Mrs May acknowledged the agreement had involved "difficult and sometimes uncomfortable decisions.
"I understand fully that there are some who are unhappy with those compromises but this deal delivers what people voted for and it is in the national interest," she said.
She added: "As PM my job is to bring back a deal that delivers on the vote of the British people, that does that by ending free movement, all the things I raised in my statement... ensuring we are not sending vast annual sums to the EU any longer, ending the jurisdiction of the European Court of Justice, but also protects jobs and protects people's livelihoods, protects our security, protects the union of the United Kingdom.
"I believe this is a deal which does deliver that, which is in the national interest, and am I going to see this through? Yes."
Mrs May compared herself to her stubborn but effective cricketing hero as she told reporters: "What do you know about Geoffrey Boycott? Geoffrey Boycott stuck to it and he got the runs in the end."
In response, the legendary cricketer said he was "flattered" by the comparison.
Asked if she would contest a confidence vote and carry on as Prime Minister if she won by a single vote, Mrs May said: "Leadership is about taking the right decisions, not the easy ones."
Discussing the potential outcomes if the Commons failed to back the deal she also ruled out the option of a second referendum.
Speaking to reporters outside Parliament, Mr Rees-Mogg said he believed the 48 letters needed to trigger a vote of no confidence would be submitted, but declined to say how soon.
If Mrs May was ousted as leader, a contest to choose a successor could be completed "not in months, but weeks", he said.
He refused to name his preferred successor, but he identified Mr Raab, Ms McVey, Boris Johnson, David Davis and Penny Mordaunt as potential candidates.
"This is nothing to do with the ambition of Brexiteers," he said. "It is everything to do with the ambition of Brexit for this country."
Dismissing Mrs May's plan, he said: "This is not Brexit. It is a failure of Government policy. It needs to be rejected."
Outside of Westminster, EU negotiators will wait until the summit on November 25 of the other 27 EU countries to give the deal their seal of approval.
EU officials have played down any chance of renegotiating the Brexit deal.
Germany's Angela Merkel also made it clear she has no interest in reopening the process again.