Speaking at the G20 summit in China, Mrs May said her government is examining all possible options
A points-based immigration system championed by Brexit campaigners has been dismissed by Theresa May, who said it was "not a silver bullet" to reducing the number of people coming to the UK.
An Australian-style system was one of the key policy pledges made by Vote Leave campaigners including Boris Johnson during the referendum campaign.
But the British Prime Minister said there were questions over whether such systems worked as she vowed that the free movement of EU citizens could not continue in its current form after the Brexit vote.
Mrs May also refused to rule out contributing funds to EU programmes after Brexit, despite money being paid to Brussels forming a major part in the referendum debate.
Speaking to reporters during her visit to China for the G20 summit, she said: "You really don't want to ask a former home secretary about the intricacies of points-based systems.
"One of the issues is whether or not points-based systems do work, and so forth.
"What I say is the voice of the British people was very clear. They wanted control in the issue of the movement of people coming in from the European Union.
"They didn't want free movement to continue as it has done in the past. We will be going out there to deliver on that."
She added: "There is no single silver bullet that is the answer in terms of dealing with immigration.
"People voted for control. What they wanted to see was some control in the movement of people from EU countries into the UK."
Mrs May repeated her desire for EU nationals to be allowed to stay in the UK after the referendum vote - but only if the rights of Britons overseas are respected.
Mrs May said: "I value the contribution that EU citizens have made and as long as we're members, there will be no change in their status. I expect to be able to guarantee their status.
"The only circumstances in which that wouldn't be possible, is if other EU countries don't guarantee the status of British citizens who are living in other EU countries. And I think it's absolutely wrong."
But Mrs May refused to divulge any details of exactly what system of control the UK would be operating after the country leaves the EU, other than removing people who arrive or stay in the country illegally.
"You have to look across the board, you have to look at the whole range of issues," she said, "not just how you bring control, the rules that have been coming in but also making sure you're rooting out the problems in the system. And obviously dealing with people if they're discovered here illegally."