The men, two of which are said to be directors at Dulwich-based Pinpoint Press, were arrested on suspicion of fraud by false representation and copyright theft.
A City of London Police spokesman confirmed that two of the men arrested were "directly linked" with "a print company".
Of the three men arrested, one, aged 34, was arrested on 21 June, while the other two, aged 54 and 57, were arrested on 22 June. All three remain on police bail.
A spokesman for Pinpoint Press said that those involved had cooperated fully with the police and have not been charged to date.
According to the police, around 1.4m printed inlays were seized during the raid on the printer, which - when paired with a counterfeit DVD - would have a street value of more than £2.5m.
The raid was part of a joint investigation by the police and the Federation Against Copyright Theft (FACT).
Meanwhile, a second team of officers moved in on a residential premises and found 144 burning trays, capable of producing around 70,000 counterfeit discs a week.
Detective chief inspector Dave Clark, from the City of London Police's Economic Crime Directorate, said illegal DVD production "on this huge scale" could produce both illicit earnings and the potential revenue that funds other elements of organised crime, including drug and human trafficking.
He said: "Counterfeiting can seem like a victimless crime but the reality is it causes huge damage to the film and music industry and has a detrimental effect to the UK economy, both on employment and tax revenue.
"This is why we will continue to operate in close partnership with FACT and work to ensure the criminal networks who run these factories are dismantled and the perpetrators brought to justice."
Eddy Leviten, head of communications at FACT, said that in recent years, organised criminals had moved into DVD piracy as a lucrative means of generating profit.
He said: "This illegal trade impacts directly on the livelihoods of tens of thousands of people in the UK, as well as causing losses of half a billion pounds a year to UK businesses."
FACT works with police, trading standards and the Serious Organised Crime Agency to target those running sophisticated counterfeiting operations across the UK.
Leviten added: "As part of ongoing efforts to tackle the supply of counterfeit DVDs, FACT is raising awareness among the printing industry as the printed inlays that accompany the DVDs are an integral part of the packaging and greatly enhance their sale.
"There is evidence that these inlays are largely printed on commercial presses for organised criminal networks and FACT is reaching out to the printing industry to raise awareness and to act if approached to print such material by contacting Crimestoppers on 0800 555 111, where the call is anonymous."
