The Home Secretary said the principle of free movement within the EU has allowed jobless citizens to move countries in search of work and benefits, putting pressure on public services and infrastructure.
She added that the events of this summer, which have seen hundreds of thousands of migrants and refugees risking their lives to reach Europe, should act as “wake-up call” to EU leaders.
Earlier this week official data showed net migration in to Britain had reached a record high, hitting 330,000 in the year to March.
Mrs May said the figure was “far too high” and “simply unsustainable”.
She added: “Reducing net EU migration need not mean undermining the principle of free movement.
“When it was first enshrined, free movement meant the freedom to move to a job, not the freedom to cross borders to look for work or claim benefits. Yet last year, four out of 10 EU migrants, 63,000 people, came here with no definite job whatsoever.”
Earlier this month Mrs May visited Calais to inspect new security measures preventing migrants from reaching England via the Channel Tunnel.
She also blamed the “European system of no borders” for exacerbating the migration crisis which has dominated Europe this summer. This is a wake-up call for the EU. Its leaders must consider the consequences of uncontrolled migration – on wages, jobs and social cohesion of the destination nations; on the economies and societies of the rest; and on the lives and welfare of those who seek to come here,” she said.
“If we want to control immigration we must take some big decisions, face down powerful interests and reinstate the original principle underlying free movement within the EU.”
Unprecedented numbers of migrants are reaching EU borders, surpassing 100,000 in July alone and reaching more than 340,000 this year so far.
Italy and Greece are struggling to cope with the daily influx of migrants and refugees, while Macedonia has declared a state of emergency.
CBI director general John Cridland said: “The evidence shows that the vast majority of people coming from the EU to the UK come to work and benefit our economy.
“Our hospitals and care homes couldn’t function without overseas workers; building sites that we need to deliver more homes and big infrastructure projects would also stall,.
“But the system must be about freedom to work, not for the minority who do not contribute, so the Government should continue to work with our European partners to make sure the rules are fit for purpose for everyone.
“We’d be concerned if EU workers had to be hired for a job before coming to the UK though, as this would cause issues for firms without the capacity to advertise and recruit across the whole of Europe.”
An SNP spokesman said: “Theresa May’s comments have less to do with the employment status of immigrants and everything to with her own job prospects as a future leader of the Tory party.”