Emergency services were first called to the site off Mount Street at about 7.40pm on Sunday.
More than 30 fire appliances were deployed to the scene and 8,000 litres of water a minute were being pumped from a nearby canal at one point, said fire chiefs.
In a statement, the brigade said: “On-site fire safety procedures helped us in our initial attack on the fire,” adding investigators would start work on Monday to try to work out what started the blaze.
“Firefighters have faced challenging conditions at the site, including the amount of smoke created,” the spokesman added.
Nearby residents and businesses have been asked to keep windows closed, while there have been no reports of any injuries.