Detectives investigating possible criminality before and during the Grenfell Tower disaster have interviewed leaders of the London fire brigade (LFB) in relation to health and safety offences that may have contributed to the deaths of 72 people.

The Metropolitan police interviewed the LFB under caution as a corporate body, bringing the number of such interviews to 17 so far, two years and three months after the tragedy. Unnamed others have also been questioned in relation to offences of gross negligence manslaughter and corporate manslaughter, but police have said charges are unlikely to be brought until 2021, after the conclusion of the parallel public inquiry into the 14 June 2017 fire.

Det Supt Matt Bonner, the senior investigating officer of Operation Northleigh, established to investigate the Grenfell fire, told the bereaved, survivors and residents on Monday: “I expect that this number will continue to rise in the forthcoming weeks and months as further progress is made.”

Dany Cotton, the commissioner of the LFB, said she recognised that survivors and the bereaved needed answers and that the fire service was committed to assisting investigators.

“We have always been subject to the Metropolitan police investigation and I want to ensure it is accurately and publicly known the brigade has now, voluntarily, given an interview under caution,” she said.

Criminal charges of breaching the Health and Safety at Work Act would require prosecutors to prove the defendant had not done all that was “reasonably practicable” to prevent the possibility of danger. Bodies charged with corporate manslaughter must be shown to have managed their activities in a way that caused death and breached their duty of care.

Cotton reiterated the LFB’s defence on Monday that her service was put in an impossible position by the way the building was designed and built. “We must all understand what happened and why to prevent communities and emergency services from ever being placed in such impossible conditions ever again,” she said.

Breaches of health and safety law are punishable by unlimited fines and up to two years in jail if individuals are charged. Corporate manslaughter is punishable by fines and gross negligence manslaughter can result in directors being jailed.

The conduct of the LFB was heavily criticised during the first phase of the separate public inquiry into the disaster. Cotton shocked survivors when she told the inquiry that she would do nothing differently with the benefit of hindsight. In evidence last September, she said she would not train firefighters for a cladding fire any more than she would train them for “a space shuttle landing on the Shard”.

“It is only right that serious questions are being asked of the LFB,” said Grenfell United, an organisation for the bereaved, survivors and community of Grenfell Tower. “It’s been 27 months since the fire that killed 72 people. The first inquiry report is yet to be published and so far there have been no arrests. We have been very patient but in the months ahead we need to see organisations and individuals being brought to account, lessons being learned and changes being made.”

Lawyers for the bereaved, survivors and residents have urged the inquiry chairman, Sir Martin Moore-Bick, to conclude the LFB breached its policies and legal duties in failing to plan or train for the foreseeable event of a fire such as that at Grenfell. Danny Friedman QC told the inquiry that shortcomings in the way 999 calls were handled had “undeniably contributed to people dying” and cited “callers being offered the choice whether to stay or go when there was none”. He said fire brigade commanders had failed to respond to what they could see happening in front of them as the fire jumped from flat to flat.

The inquiry’s report into what happened on the night of the fire is due to be published next month and the second phase of the inquiry examining the refurbishment of the tower with combustible materials is scheduled to start in January.