The Home Office is to launch an independent review of modern slavery laws after its own research revealed the crime costs the UK up to £4.3bn a year.

The report, published on Monday, estimates that each instance of the crime costs around £330,000, including support, lost earnings and law enforcement.

Modern slavery, including labour exploitation, sexual exploitation and domestic servitude, is estimated to cost the UK between £3.3bn and £4.3bn, with the range reflecting uncertainty around the number of victims, which is put between 10,000 and 13,000 people.

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Publishing the report, the Home Office said it would launch a review of the Modern Slavery Act 2015, led by the Labour MP Frank Field, the Tory MP Maria Miller and the crossbench peer and former high court judge Lady Butler-Sloss.

Butler-Sloss said: “The exploitation and enslaving of men, women and children across the world and within the UK is one of the most shocking crimes and one of the most profitable. The Modern Slavery Act is a splendid piece of legislation but it is very important to review how well it is being implemented and how it could be improved.”

Announcing the review, the crime minister, Victoria Atkins, said: “The prime minister established this country as a world leader in this fight against modern slavery through our ground-breaking laws and law enforcement approach.

“However, as this awful crime is evolving, it is our responsibility as citizens, businesses and governments to do all we can to stop exploitation. This independent review will help us identify what more we can do to tackle this terrible, global injustice by enhancing the Modern Slavery Act where necessary.”

The review will examine the nature of modern slavery offences, provisions for legal access and compensation to victims and improving the support given to child victims.

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Legislation currently requires every business with an annual turnover of £36m and above to publish a statement on its website outlining what it is doing to prevent and tackle modern slavery in its operations and supply chain.

The review will also look at what else can be done to strengthen the legislation and minimise the risk that goods and services available in the UK are produced through forced labour and slavery.

The Home Office also confirmed a £2m extension of the Independent Child Trafficking Advocates (ICTAs) scheme, which works with trafficked children.

There are currently three sites in Greater Manchester, Hampshire and Wales piloting the scheme in partnership with the children’s charity Barnardo’s, and more are to be added from autumn 2018, beginning with the West Midlands.