David Cameron is facing a fresh assault on his EU renegotiation deal, with figures expected to show net migration is still running near record levels.
Cabinet minister Iain Duncan Smith predicted the latest official data would highlight an "ever-increasing" flow from eastern Europe and insisted the Prime Minister's reforms would have no real impact.
The comments, in an interview with the Guardian, came as tensions between senior Tories threatened to escalate further just days after the starting gun was fired on the referendum.
Downing Street hit back at Justice Secretary Michael Gove for suggesting the package secured by Mr Cameron was not legally binding and could be ignored by the European Court of Justice.
It has been confirmed that, in line with guidance issued by the Cabinet Secretary, Mr Gove and other Brexit-supporting ministers are now barred from receiving government papers relating to the referendum struggle.
Number 10 was also forced into an embarrassing apology after incorrectly including the name of special forces general Sir Michael Rose in a letter from senior military commanders warning that leaving the EU would risk Britain's security.
Launching the Conservatives In campaign in central London, Mr Cameron urged activists to prepare for a major fight.
Flanked by colleagues including Foreign Secretary Philip Hammond, Transport Secretary Patrick McLoughlin and Europe minister David Lidington, the premier warned: "This is going to be a battle for Britain, a battle for the future of our country, the sort of country that we want for our children and our grandchildren.
"This is about what sort of a country we are going to be - how wealthy we can be, successful in a single market, or how much uncertainty you can have outside.
"How safe we can be, working with our partners in the EU in combating crime and terrorism. Or how unsafe we can be outside it."
The remain campaign was given a boost when head of the International Monetary Fund Christine Lagarde warned that leaving would hurt the UK and the EU.
"My hunch ... is that it is bound to be a negative on all fronts," she told CNN.
The focus is set to return to the impact of membership on immigration as the Office for National Statistics publishes its latest figures covering the year to September.
In the year to June, net migration - the difference between the number of people arriving and leaving - stood at an estimated 336,000. That was a third up on the previous 12 months, and more than three times the Government's target of a maximum 100,000.
Net migration of EU citizens was around 180,000.
Mr Duncan Smith stressed that he had not yet seen the statistics, but said: "I would lay even money that they follow the trend over the past two quarters showing an ever-increasing number of migrants from eastern Europe.
"So is this agreement negotiated in Brussels going to limit the numbers coming into the UK? My answer to that is no. The truth is, there is one clear way that we could be sure to deliver on that manifesto commitment - and that's to regain control of our borders."
He conceded that the "emergency brake" on EU migrants accessing in-work benefits for up to four years, which can remain in force for seven years, would "send a signal" that people should contribute before claiming benefits.
But he suggested that the arrangement could actually cause a short-term spike in immigration, as it could not come into force until April 2017 at the earliest.
"Anyone with any thought of coming to work in the UK in the foreseeable future will have a motivation to get over here and establish residency (even if only for a week) as that would in all likelihood qualify them for an exemption from the brake later," Mr Duncan Smith said.
He insisted failure to address immigration concerns could result in the rise of extreme right-wing parties.
"If you do not control your borders, my observation is that you get parties led by people like Marine Le Pen and others who feed off the back of this, and ordinary decent people feel life is out of control," he said.