The Prime Minister and the UK's two leading church leaders, the Archbishop of Canterbury and the Archbishop of Westminster, all made fresh pledges to tackle human trafficking and forced labour at a service in memory of abolitionist William Wilberforce.
Campaigning by William Wilberforce, a Christian, led to the passing of the landmark Slave Trade Act of 1807 which made the British Empire and Transatlantic slave trades illegal.
At the service Theresa May pledged to put Britain at the forefront of the fight to bring the perpetrators to justice.
Mrs May said the Modern Slavery Act which came into force last year meant Britain now had some of the toughest penalties anywhere in the world.
"As Prime Minister, I want Britain at the forefront of this fight, leading the world with our efforts to stamp out modern day slavery and human trafficking.
"This is a global phenomenon that knows no geographical boundaries, crossing not just borders but over the internet.
"So we need a radical domestic and international approach to target every aspect of this despicable trade and strip the slave drivers of the profit they make out of human suffering by putting them behind bars.
"We will work tirelessly, relentlessly pursuing the perpetrators of these appalling crimes so that victims of slavery can go free."
The Archbishop of Canterbury, Most Rev Justin Welby, said there were "possibly tens of thousands" of people in Britain who were subject to slavery, but that too often it went unnoticed.
A report released on Wednesday said around 13,000 people were trapped as victims of modern slavery.
"Slavery is all around us and yet we are too blind too often to see it," he said.
"We drive past slaves at the car wash, we encounter slaves in the street doing routine jobs for which they receive virtually nothing. It is all around us."
Cardinal Vincent Nichols, the leader of Catholics in England and Wales, praised the Government's "leadership" but urged ministers to do more to help children in the Calais "Jungle" who were at risk of exploitation by people traffickers.
"I hope our Government - known for its leadership in opposing human trafficking - and the government of France will very quickly improve the effectiveness of the the asylum procedures, particularly for children there who may have the right to be here," he said.