"It's been an absolute nightmare," the Party of Five star says, his voice shaking, in a videotaped statement released to RadarOnline on Tuesday. "First of all, I want to say [the incident] actually did happen. It was one of the worst days of my life. I thought I was going to die. Thank God I made it out alive."
"I had a gun put to my head," he continues. "I had my family threatened. We're working closely with the Palm Springs Police Department to get the rest of the guys. There's one guy in custody. There's two more out there."
London, 37, a recovering drug addict, has been embroiled in a custody battle with his ex-wife Melissa over their son Lyric, 3. But the two have apparently reconciled, since it was later revealed that Melissa, who also has allegedly battled drug use, was with London in the initial stages of the alleged kidnapping.
In the statement, London, 37, also lashes out at his mother, twin brother Jason and his brother's girlfriend, saying they were spreading "outrageous lies" about the incident. London, who says he hasn't spoken to his family in six months, sent legal threats to his family to stop talking to the press. He also says he's seeking restraining orders against them.
Reached for comment Monday, Jason told PEOPLE, "I'm glad my brother’s okay, but I have serious questions about what transpired. His health is our number one concern."
Asked if there was any reason to doubt London's version of events, Palm Springs Police spokeswoman Melissa Desmarais said: "No, not at this point. Our investigators had enough information to arrest a suspect and the investigation is ongoing."
The suspect, Brandon Adams, 26, has already been charged with kidnapping, robbery, possession of stolen property, vehicle theft and carjacking.
London opened up to PEOPLE earlier this year about his struggle to stay sober and his financial troubles.