The fire has now been put out. Fire crews will remain on site damping down the blaze.
Around 70% of the building has been destroyed and electricity supplies have been cut off for safety purposes.
The cause of the fire is not yet known.
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Highways England says the closures are taking place during the summer holidays as the roads around Birmingham are much quieter.
A dry start with sunny intervals.
Kumran Ghalib stayed in hiding abroad while his 18 accomplices were jailed for a combined total of more than 200 years.