The contents of the containers were clearly of UK origin
The UK is working with Brazilian authorities to return more than 1,400 tonnes of toxic waste to Britain, the Environment Agency has said.
Head of waste Liz Parks said plans were being made to bring back the rubbish, but it could take a number of weeks.
An inquiry into how the waste, including syringes, condoms and bags of blood, was sent to three Brazilian ports has been launched by the UK.
The Environment Agency says those responsible could face prosecution.
It confirmed its Brazilian counterpart has named Worldwide Biorecyclables and UK Multiplas Recycling - both based in Swindon - as being involved, but would not confirm or deny whether the agency was investigating the two companies.
Ms Parks told the BBC's Newshour she understood the waste, found in about 90 shipping containers, was currently being held by the Brazilian authorities.
"They haven't yet released it, as far as I'm aware. But arrangements are being made for that to happen. And it will take a number of weeks for the waste to be returned," she said.
She also warned the British courts took the dumping of hazardous waste very seriously.
"We do prosecute people. We've had a number of successful prosecutions in recent years.
"And in fact in the crown court, people can be fined unlimited amounts and prison sentences are imposed."
On Saturday, Brazil demanded the waste be sent back to Britain.
Roberto Messias, president of the Brazilian environment agency, Ibama, declared that Brazil was "not a big rubbish dump of the world".
The agency also said the arrival of the toxic cargo had violated the Basel Convention on the movement of hazardous waste, of which both the UK and Brazil are signatories, which came into force in 1992.
Ingrid Oberg, regional chief of Ibama, later told the BBC the cargo mainly consisted of domestic waste.
"It's a lot of food containers and cleaning product containers. We found old clothes, shoes, papers, a lot of old newspapers.
"In some of the containers recently found there were also some technological products, like DVDs, pieces of computers, plastic stuff. But mainly it's domestic garbage."
As well as the presence of syringes, condoms and bags of blood, the rubbish was deemed dangerous because the contents of the containers were going rotten.
"There were larvae and then there's a big risk of contamination," said Ms Oberg.
"We are taking care so that it's not taken out of the containers. So it doesn't bring any contamination to our soil," she added.
Reports in the UK media say the waste was sent from Felixstowe in England to the port of Santos, near Sao Paulo, and two other ports in the southern state of Rio Grande do Sul.
It has also emerged that two companies named by Brazil as suspected exporters of the waste are owned by a Brazilian.
The director, who is based in England, told BBC Brazil the containers should have contained plastic for recycling and any other contents were the responsibility of his suppliers.