EU rules on free movement of labour make it harder to control immigration, Home Secretary Theresa May has admitted.
However, in her first major intervention in the Brexit battle, Ms May insisted the task was not impossible as she tried to distance herself from an official Treasury study showing that immigration would soar by three million by 2030.
"Yes, free movement makes it harder to control immigration, but it does not make it impossible to control immigration," the Home Secretary told the BBC's Andrew Marr Show.
Ms May. who has kept a low profile in the referendum debate since backing Prime Minister David Cameron's Remain stance, would not be drawn on a Government document saying immigration would jump by three million.
"That was an independent figure, that was an independent estimate," the Home Secretary said of the Office for National Statistics' prediction of a steep rise in immigration, which was put out by the Treasury as part of the Government's claim that Brexit would cost each household £4,300 a year.
Ms May insisted the ONS was independent of Government.
The Cabinet heavyweight denied the prominence of the royal family during the visit of US president Barack Obama as he delivered a strongly anti-Brexit message amounted to an establishment "stitch-up".
The Home Secretary acknowledged migrants would look at the rises in the national living wage when making a decision on whether to come to Britain.
"I think, yes, obviously, the national living wage is going up and people look when they are going to move at what they are going to earn.
"But, of course, what we have at the moment is, we see migrants coming in to take jobs that people in the UK aren't taking. And, of course, one impact of the increased living wage could be that more people resident in the UK take some of these jobs," Ms May said.
The Home Secretary insisted Britain had won a landmark concession from Brussels on immigration.
"We've got agreement that the EU will overturn judgments of the European Court of Justice that mean that it is easier for people to abuse the free movement rules.
"I think immigration is too high, but controlling immigration is hard, and it is hard whether we are inside the European Union, or outside the EU.
"We don't know what the system would be if we were outside the EU because that is one of the uncertainties.
"Control of our borders and immigration policy are two different things.
"If we were to be outside of the EU and still want the sort of access to the single market that people talk about, then actually if you look at other countries that people talk about they have to accept the free movement rules without any say over those rules," Ms May said.