Labour has called on the government to stop UK supermarkets stocking food produced by slaves, after a Guardian investigation into forced labour in the Thai seafood industry.

Yvette Cooper, the shadow home secretary, said the coalition's modern slavery bill did not go far enough to turn up the pressure on UK retailers to shun products linked to forced labour. The opposition is pushing for new requirements on firms to declare any use of slavery in their supply chains but the government prefers a voluntary approach.

David Cameron's spokesman said on Wednesday it was up to consumers whether they choose to eat prawns that had been produced through the work of slaves.

The Guardian revealed on Tuesday that slavery is integral to the production of prawns available in leading global supermarkets including Tesco, Walmart, Costco and Carrefour.

Its six-month investigation discovered that slaves are being forced to work in Asia for no pay for years at a time, under threat of extreme violence, in the production of seafood sold by major US, British and other European retailers.

"The allegations in this investigation are shocking," said Cooper. "Trafficking people into slavery is an abhorrent crime and the international community should work together to stamp it out entirely. We have called for greater transparency in supply chains to ensure products that have been produced through forced labour do not end up on our shelves. The government's modern slavery bill doesn't go far enough to address this and we will be pushing for changes to ensure companies are more accountable for the actions of those in their supply chain."

Frank Field, the Labour MP who chaired the parliamentary committee on the slavery bill, said supermarkets must "immediately cease" using suppliers linked to seafood slavery.

He also blamed Downing Street for resisting new reporting requirements for fear of increasing red tape, even though most companies are not opposed to the transparency initiative.

"It was clearly the home secretary's wish to include a supply chain clause because she wrote about this, but that wish is being blocked," said Field. "It is coming from No 10. There is a perceived belief what business wants without actually knowing. We marshalled a huge amount of support from business for a supply chain clause. If they paid a bit of attention they would know most business wanted them to do this."

There would be a "huge effort" in the Commons and Lords to introduce amendments about slavery in supply chains, Field added.

Lady Butler-Sloss, a former senior judge who also sat on the committee, said the Guardian's investigation underlined the need for action on slavery in company supply chains.

Butler-Sloss, a trustee of the Human Trafficking Foundation, said: "The government has come a very long way on the bill and I am absolutely delighted it is being passed, but so far as the supply chain is concerned it is very weak. The brilliant detective work by the Guardian is a very good example of why actually we need the quite modest amendment we recommended, which is to add modern slavery to human rights in the Companies Act."

A Home Office spokeswoman said slavery was not a problem that can be solved by legislation alone or by the end of the parliament. "It needs the engagement and long term commitment of all sections of society," she said. "Companies have a social responsibility to ensure that those they do business with are not involved in the exploitation of others. If businesses take no action they risk both their reputation and profit.

"Today, the home secretary and minister for modern slavery Karen Bradley, have hosted a roundtable with key business leaders to look at how the government can work with businesses to eliminate forced labour and exploitation from supply chains."

In contrast to the reaction of the US, which is considering blacklisting Thailand over slavery in its seafood industry, Downing Street indicated on Wednesday that it preferred to leave the matter to the choice of shoppers.

Asked whether supermarkets should stop stocking seafood produced with the help of forced labour, Cameron's spokesman said: "Consumer standards and retail standards and social responsibility is often driven by consumers and rightly so."

He could not say whether Cameron himself would be happy to eat prawns where slavery had been used in their production.

The Home Office said it took the issue extremely seriously and had not ruled out legislating to make reporting requirements tougher for companies. Theresa May, the home secretary, is meeting business leaders on Wednesday to discuss eradicating slavery from supply chains. However, it is understood the voluntary approach is favoured at present.

The government is bringing in new penalties to deter modern slavery through the bill unveiled in the Queen's speech, but this has been criticised for its narrow focus on slavery in the UK and failure to tackle the problem of goods produced through slavery abroad.

However, the Home Office said the government wanted to work collaboratively with businesses to support them to eliminate forced labour in supply chains "in a way which does not place additional burdens on them".

It also pointed out that the EU was likely to enact new laws in 2016 forcing companies to report on human rights in their "business relationships", which could mean an expectation on firms to audit their supply chains for signs of slavery.

"In taking any further action in this area, the government is, therefore, mindful of existing requirements on business and possible future changes to the business reporting regime," the Home Office said.

"We intend to build on the existing legislative framework, and work with business to establish what more can be done to raise awareness among their workforce and their subcontractors, and develop an evidence base on best practice. The home secretary is meeting with business leaders in June to help assess the most effective way forward.

"In doing so, we recognise the complexity of supply chain issues, particularly where they involve links with business overseas and where the influence of UK-based companies is diminished. Cross-government action is being taken to bring businesses together to discuss the challenges and opportunities in tackling modern slavery in supply chains."