ESP Smile has been approached for comment.
A force spokesperson said they evacuated nearby buildings, and that people living nearby should stay indoors and keep their windows closed for their own safety.
Dorset and Wiltshire Fire and Rescue Service said it was dealing with a large warehouse fire and currently has 10 fire engines at the scene, along with other specialist vehicles.
Dozens of residents have written on social media that they felt their homes shake following the explosion.
Jason O’Grady, head coach and owner of Swindon Martial Arts and Fitness, located about 200 metres (656ft) from the site, said staff running lessons earlier heard “a massive loud bang” and “bits of ceiling tile fell down on everybody”.
Mr O’Grady, who was not at work at the time, said staff had initially thought the building had been hit by a car, and that a large crack had appeared along the top of the wall.