The Daily Mail reports Collins was arrested on suspicion of supplying class A drugs and questioned by Wiltshire Police over possession of a class B drug.
The 37-year-old musician was released on bail soon after his apprehension.
The United Kingdom's Misuse of Drugs Act states that Class A substances include cocaine, meth, psychedelics and opioids like heroin and oxycodone. Class B drugs include marijuana, amphetamines, sedatives and Ritalin.
Collins is Phil Coliin's first son with wife Andrea Bertorelli. Like his father, he grew up to be a musician and is the lead singer and drummer of the rock band Sound of Contact.