The government has placed the builder that oversaw the disastrous refurbishment of Grenfell Tower on an official list of firms recommended to build high-rise housing, a move that has sparked fury among survivors.

Rydon was the main contractor on the recladding which spread the fatal blaze that claimed 72 lives in 2017. The decision less than three years later to name it as one of the firms on a new £30bn seven-year construction framework agreement has been attacked as “adding insult to injury” by the bereaved and survivors.

Rydon will face intense scrutiny in the second phase of the public inquiry into the disaster, which will begin in the new year after the first phase last week concluded that the £10m refurbishment of Grenfell broke building regulations.

All the companies involved in the refurbishment are also understood to be part of the investigation by the Met police for potential criminal offences including manslaughter and corporate manslaughter. Rydon has been named as one of 12 firms on the framework agreement that helps public sector bodies find building companies. The firm more than doubled its post-tax profits in the year after the disaster to £16.6m.

“It is totally unacceptable that Rydon, one of the companies required to answer questions for its role in the refurbishment of Grenfell Tower, would be put on a government list that promotes it as a reputable contractor for other high-rise towers,” said a spokesperson for Grenfell United, the main group representing bereaved families and survivors.

“It makes us question the government’s intention to learn the lessons of Grenfell. [The housing secretary] Robert Jenrick must suspend Rydon from this list and explain how the contractor under investigation for Grenfell ended up there.”

A government spokesperson said: “There is absolutely no guarantee of a company securing government contracts just because they are on a framework. Under existing EU rules, we are not legally allowed to preclude Rydon Construction from bidding for government contracts.”

If a company is charged with an offence they can be excluded from bidding for work, officials said.

Rydon declined to comment on its selection, which was first reported by Construction News.

The move came as Jacob Rees-Mogg, the leader of the House of Commons, was forced to apologise for saying he would have evacuated the burning building as it was “the common sense thing to do”.

Survivors described his remarks as “extremely painful and insulting” and the Labour leader, Jeremy Corbyn, said they were “crass” and “insensitive”. Dozens of people were trapped by smoke and flames and were repeatedly told to stay put by 999 call operators.

On Tuesday, Rees-Mogg said: “What I meant to say is that I would have also listened to the fire brigade’s advice to stay and wait at the time. However, with what we know now and with hindsight I wouldn’t and I don’t think anyone else would. I would hate to upset the people of Grenfell if I was unclear in my comments.”

Also on Tuesday, the London fire brigade commissioner, Dany Cotton, told the London assembly that she feared firefighters and commanders could not be trained to tackle cladding fires similar to Grenfell.

“I still have concerns that even though we have a far greater understanding of that [the spread of cladding fires], it would be very difficult to implement training to respond to some of these situations because it is still such an extraordinary event of such a big scale that we still have huge concerns about fires in those types of buildings.”

Cotton was previously lambasted for claiming that preparing a training package for a Grenfell-style fire would have been like planning for the “space shuttle landing on the Shard [skyscraper]”. Asked why a 2016 London fire brigade (LFB) document detailing the risk of high-rise cladding fires had not been disseminated, she said: “I don’t know why.”

Cotton has resisted calls to quit in the wake of last week’s public inquiry report into the night of the disaster, which found the LFB’s failure to prepare and plan for a cladding fire and evacuation was “gravely inadequate” and a breach of national guidance. Sir Martin Moore-Bick, the chair of the Grenfell inquiry, said the LFB was guilty of an “institutional failure” to inform firefighters about the risks of cladding fires before the disaster and said “the LFB is an institution at risk of not learning the lessons of the Grenfell Tower fire”.