Part of the boiler house at the power station in Oxfordshire gave way during demolition work on 23 February 2016, killing Christopher Huxtable, Kenneth Cresswell, John Shaw and Michael Collings.
A pre-inquest hearing at Oxford Coroner's Court yesterday (31 January) was told that the HSE and TVP had launched a joint investigation to consider corporate manslaughter, gross negligence manslaughter and health and safety offences.
Detective chief inspector Craig Kirby, the senior investigating officer who is leading the investigation, told the inquest: "As the investigation has progressed, a number of significant witnesses have been identified and interviewed.
"A number of individuals and companies suspected of committing offences have been identified and voluntarily interviewed under caution."
He said he did not know how long the investigation would take but "an initial file was submitted to the CPS [Crown Prosecution Service] at the end of December for investigative advice".
Kirby added: "Clearance of boilers one and two has been completed, and independent contractors continue to clear boilers three and four. This work is expected to be completed by spring 2018.
"TVP and HSE remain committed to carrying out a thorough investigation to ascertain if any criminal or health and safety related offences have taken place."
After the hearing James Howard, director of demolition contractor Coleman and Company, which was responsible for decommissioning the site when the accident happened, said the firm had launched its own investigation.
"We commissioned our own investigations which, in our view, clearly show why and how units one and two of the boiler house collapsed. We believe the findings highlight industry-wide practices that need to be challenged and reviewed," he said.
Howard said the company would be writing to the HSE and the police to share these preliminary findings.