Crane driver Jonathan Cloake and local resident Micheal Alexa died in September 2006.
Alexa was killed by the falling crane while washing his car next to the south London site.
The four-day inquest can finally be heard after the Crown Prosecution Service decided not to pursue manslaughter charges against Falcon Cranes who owned the machine.
The Battersea disaster was one of a series of crane failures which led to a long-running campaign to improve the industry’s safety record.
The hearing is scheduled to last four-days at Westminster Coroner’s Court