She said a new UK cabinet taskforce would tackle the "sickening and inhuman crimes" while £33m from the aid budget would fund initiatives overseas.
The most recent Home Office estimates suggest there are between 10,000 and 13,000 victims of modern slavery in the UK, with 45 million estimated victims across the world.
Victims are said to include women forced into prostitution, "imprisoned" domestic staff and workers in fields, factories and fishing boats.
Mrs May said: "From nail bars and car washes to sheds and rundown caravans, people are enduring experiences that are simply horrifying in their inhumanity.
"Vulnerable people who have travelled long distances, believing they were heading for legitimate jobs, are finding they have been duped, forced into hard labour, and then locked up and abused.
"Innocent individuals are being tricked into prostitution, often by people they thought they could trust. Children are being made to pick-pocket on the streets and steal from cash machines."
In 2014, the Home Office estimated there were between 10,000 and 13,000 potential victims in the UK - just 2,340 of those were officially reported and recorded.
(Sources: Independent Anti-Slavery Commissioner Strategic Plan 2015-2017 and Modernslavery.co.uk)
Mrs May said a review to mark the first anniversary of the Modern Slavery Act found there had been 289 modern slavery offences prosecuted in 2015 - and a 40% rise in the number of victims identified.
She added that the first government taskforce on modern slavery would see ministers "get a real grip of this issue right across Whitehall and co-ordinate and drive further progress in the battle against this cruel exploitation".
Her Majesty's Inspectorate of Constabulary will also be asked to carry out an investigation to make sure that all police forces in England and Wales "treat this crime with the priority it deserves".