There is no doubt that slavery is still a thriving business across the world. According to the International Labour Organisation, an estimated 21 million people across the world are trapped in some form of forced labour and other types of modern-slavery, feeding a booming industry in human exploitation generating profits of more than $32bn each year. The United Nations estimates that people-trafficking is the third biggest criminal industry behind guns and drugs.

In recent years there has been a growing awareness that modern-day slavery is largely a labour and economic, as well as a human rights issue, and that the worst forms of human exploitation continue to lurk in the murky depths of many global supply chains. Slavery isn't a word that any business wants to be linked with.

So far the association between global brands and slave labour comes largely from damaging media exposés – such as last week's story on the sugar giant Tate & Lyle, accused of child labour on plantations in Cambodia, allegations which the company has denied.

Yet interesting models for how to get businesses to engage with the problem of forced labour are starting to emerge. Since 2006, more than 170 global companies have signed up to the Athens Ethical Principles, where signatories pledge to ensure their own businesses are slavery-free and declare zero tolerance for dealing with other corporations benefiting from human trafficking.

In California the Transparency in Supply Chains Act, which came into force last year, legally requires companies doing business in California to report on what they are doing to eradicate slavery from their product lines. The act stipulates that larger companies must make this information public through a disclosure on their websites.

In Brazil an aggressive anti-slavery strategy launched by the government in the mid-90s has led to a controversial yet seemingly effective name-and-shame strategy towards eliminating slavery from major industries.

Thousands of Brazilians and labourers from neighbouring South American countries are thought to be trapped in slavery in Brazil's booming agrarian, mining and materials sectors. Last year, Greenpeace released a report linking Brazil's charcoal industry, which fuels iron ore smelters producing metals for the international car manufacturing markets, to widespread environmental destruction and forced labour.

Since 1995, a huge labour inspections programme has carried out raids on more than 2,000 work sites, liberating an estimated 45,000 people trapped in conditions of slavery.

Ten years later the government of Luiz Inácio Lula da Silva and Brazil's private sector launched a National Slave Eradication Pact. More than 400 companies representing almost 30% of Brazil's gross domestic product have now signed up to the pact, pledging to keep their businesses free of forced labour proactively and cut commercial ties with businesses profiting from slavery.

Then for those companies that really don't play ball, there is the "dirty list", which publicly names almost 300 companies, from major brands to small enterprises, who have been found to be profiting from slave labour.

Companies stay on the list for two years, during which time they have to prove they are making concerted efforts to clean up their supply chains and pay a series of fines and unpaid labour taxes. While on it, they can't obtain credit from government and private banks and are boycotted by those who have signed up to the pact. This, say activists, is where the dirty list differs from other global business-facing anti-slavery initiatives.

"With the list, nearly all those on it have suffered from a market reaction due to the involvement of their names with cases of contemporary slavery," says Leonardo Sakamoto, founder of Reporter Brazil, an NGO that investigates companies accused of slave labour.

"Is this because the market is good and wants to protect the workers? No, the issue isn't moral but strictly business. Being on the list makes you a risky investment. It gives you a track record of public and private banks restricting your business. It has opened you to lawsuits, international trade restrictions and reputational damage on the international market."

He points out that the day news broke that labour inspectors had discovered slave labour in its suppliers' workshops, shares in the Spanish clothing giant Zara fell by almost 4% on the Madrid Stock Exchange. In December 2009, the sugar and alcohol giant Cosan appeared on the list, leading to a fall in shares and the National Bank for Economic and Social Development suspending all its dealings with the company and international purchasers, including Wal-Mart, suspending contracts.

Could and should a similar approach be taken by other governments across the world? Yes, according to Nicola Phillips, professor of political economy at the University of Sheffield, who has spent years working on forced labour and global supply chains. "I think that there is a very strong case for this kind of public intervention in other countries who could look at the stance that Brazil and many of it's businesses have taken against modern slavery," she said.

"The government devised a programme to address the issue that provided incentives to businesses and secured a good degree of 'buy-in' in many quarters, but didn't leave implementation and enforcement wholly to self-regulation by firms."

Andrew Wallis, chief executive of Unseen, a UK anti-trafficking charity says that the emphasis should now be on creating an environment where businesses feel able to explore, reveal and be helped to eradicate forced labour practices.

"I think the problem we have at the moment is that we have a culture which doesn't allow businesses to proactively and openly deal with issues of slavery in their supply chains," he says.

"What we need to do is find a way in which we can turn this around and stop corporations being too afraid to admit that they have a problem. Only then will you really get to the heart of slavery in global supply chains, because otherwise I think we have a ticking time-bomb on our hands and, unless we find a way to deal with this, the problem is only going to get worse."

This article was amended on Friday 26 July to clarify that Zara was never included on the 'dirty list' of companies.

This content is brought to you by Guardian Professional. Become GSB member to get more stories like this direct to your inbox