Free movement from the European Union will end in March 2019, Downing Street insisted as Theresa May sought to contain a Cabinet row over Brexit.
Tory Brexit tensions have heightened after Chancellor Philip Hammond and Home Secretary Amber Rudd backed transitional arrangements after the UK leaves the bloc, which suggested EU migration could continue with a registration scheme.
However, International Trade Secretary and leading Brexiteer Liam Fox said unregulated free movement of labour after Brexit would "not keep faith" with the EU referendum result and that the Cabinet had not agreed a stance on immigration.
The Prime Minister's official spokesman insisted the British Government's position remained as set out by Mrs May in her Lancaster House speech on Brexit.
"The Prime Minister's position on an implementation period is very clear and well-known," he said.
"Free movement will end in March 2019. We have published proposals on citizens' rights. Last week, the Home Secretary said there will be a registration system for migrants arriving post-March 2019.
"Other elements of the post-Brexit immigration system will be brought forward in due course. It would be wrong to speculate on what these might look like or to suggest that free movement will continue as it is now."
Number 10's intervention came as Cabinet ministers Jeremy Hunt and Michael Fallon sought to play down reports of splits within Mrs May's top team.
Downing Street acknowledged "it will take time to get immigration numbers down" but the Government remained committed to that aim.
Number 10 dismissed the idea that the UK was seeking an "off-the-shelf" model for the transitional period, as Mr Hammond had reportedly told business leaders.
"We are not looking for an off-the-shelf model. Precise details of what the implementation period looks like are for negotiation," the spokesman said.
Defence Secretary Michael Fallon said the issue of immigration policy during a transitional deal would be "one of the details" for the Brexit negotiations.
Mr Fallon, taking part in Passchendaele memorial events in Ypres, said: "It's not an argument, it's part of the negotiations.
"We have always understood that we have to ensure immigration is managed properly, that's what the public expect to see - that there are controls of it.
"That's one of the details that's going to be sorted out during the negotiations. It's not an argument raging around the Cabinet table."
Health Secretary Mr Hunt insisted the Cabinet was "completely united", telling BBC Radio 4's Today programme: "It has to be a Brexit that works for business, it has to work for the NHS, the NHS needs to recruit doctors and nurses from all over Europe and that is going to continue after we leave the European Union."
A spokesman for Boris Johnson was forced to dismiss a suggestion that the Foreign Secretary was about to quit over the way Brexit was being handled.
He said Liberal Democrat leader Vince Cable, who had referred to rumours about Mr Johnson's future, was "making this stuff up".
The Prime Minister's spokesman said the Foreign Secretary was "doing an excellent job".
Meanwhile, Mr Hammond used an interview with Le Monde to downplay claims Britain could try to become a Singapore-style low-tax economy if it does not get the Brexit deal it wants - appearing to contradict his earlier position on the UK's potential future.
He said: "I would expect us to remain a country with a social, economic and cultural model that is recognisably European."
Number 10 said the Prime Minister still believed that "no deal is better than a bad deal".
The PM's spokesman said: "It's obviously not in Britain's interests to sign up to a deal which would punish the UK.
"But what we are fully committed to doing is securing a good deal for Britain and for the European Union and we are making good progress towards it."
Shadow Treasury chief secretary Peter Dowd said: "This Government has broken down into farce.
"The Chancellor is not only disagreeing with Cabinet colleagues over Brexit, he is now in open dispute with himself given it is only his own comments on the matter in January which he is pretending to contradict."
Mr Cable said: "Philip Hammond's assurances that Britain will not become a tax haven with low-quality public services in a post-Brexit world are welcome, even if they do contradict an earlier threat he made on the subject."