Ken Cresswell, 57, John Shaw, 61, both from Rotherham, Michael Collings, 53 from Teesside and Christopher Huxtable, 34, from Swansea, died when the boiler house came down in February 2016.
A pre-inquest review hearing at Oxford Coroner's Court heard an update on Thames Valley Police's investigation.
The force said it was looking at charges of corporate manslaughter, gross negligence manslaughter, and serious health and safety breaches.
Det Ch Insp Craig Kirby told coroner Darren Salter an evidence file was passed to the Crown Prosecution Service on December 29, 2017.
Speaking after the hearing, he said: "We continue to carry out a thorough investigation in order to obtain answers for the affected families and friends who lost their loved ones, and those who were injured following the partial collapse at Didcot.
“This is an extremely wide scale and hugely complex investigation.
“To date over 1,900 witness statements have been taken by the investigative team, and a number of interviews have been conducted under caution in line with the Police and Criminal Evidence Act (1984).
“These interviews have taken a significant length of time, and further interviews will need to be undertaken.
“The joint TVP and Health ans Safety Executive investigative team continue to meet regularly with a specialist dedicated prosecutor from the Crown Prosecution Service (CPS) to ensure that all lines of enquiry are being appropriately and robustly explored.
“At this time it is not possible for us to put a timeframe on the completion of the investigation however an initial file was submitted to the CPS at the end of December for investigative advice."
It took more than six months for the men's bodies to be recovered from the site.
The coal-fired station was shut in March 2013 after 43 years of operations.
The original plan was to have the site cleared by the end of 2017.
Det Ch Insp Kirby added: “On-site recovery of evidence continues to be a key line of enquiry, to understand why the boiler house collapsed.
“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.
“The site remains a crime scene with a 24/7 police scene guard. A TVP and HSE evidence recovery team continue to work on site.
“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, and to obtain justice for the families and all those affected."