Some retailers have pledged action in response to the allegations, while others have distanced themselves from the reports or blamed third parties.
The programme, which showed Syrian refugees working 12-hour shifts in hazardous conditions, also revealed workers were being paid a little more than £1 per hour, breaking Turkish minimum wage laws.
Prior to the investigation, a spokesman for M&S said the company had found no evidence of Syrian workers employed in factories that supply it.
"So we were very disappointed by these findings, which are extremely serious and are unacceptable to M&S."
As a result of the investigation, M&S said it is offering permanent legal employment to workers, as well as remedial action in support of any Syrian daily worker shown making M&S clothes in the programme, the spokesman said.
He added: "Ethical trading is fundamental to M&S. All of our suppliers are contractually required to comply with our Global Sourcing Principles, which cover what we expect and require of them and their treatment of workers. We do not tolerate such breaches of these Principles and we will do all we can to ensure that this does not happen again."
Online fashion retailer Asos, whose products were also visible throughout the programme, said "caring about what goes on in our supply chain, wherever in the world, is not just an option, it's vital".
CEO Nick Beighton said: "The issues Panorama raises aren't with our approved factories, who we audit. It's with unapproved outsourcing to factories we don't know about. This will continue to be a problem until we know where every garment is made and however difficult, that's what ultimately we've got to achieve."
He also said it would be irresponsible to pull out of Turkey and move the work elsewhere.
"By staying in Turkey and working within the system, we are committed to building good ethics into our supply chain and in the meantime, we continue to play our part in supporting vulnerable people."
Elsewhere in the programme, a factory owner claimed he had been working on an order for Next, showing the investigators a set of pyjamas with a Next label.
However, a statement from the company said no Next production was found to be taking place in any of the factories featured in the programme.
Responding to the allegations, a spokesman for the company said: "Next was pleased to note that none of its clothes were made in any of the factories featured in the programme. The only Next item shown was a set of pyjamas and as Panorama stated, these were not made in any of the factories that were included in the broadcast."