James Brokenshire, the housing secretary, is expected to announce a consultation on banning flammable materials such as the polyethylene-filled cladding panels that fuelled the inferno at Grenfell last June.
He was speaking after a government-ordered review of building regulations, published earlier, drew widespread criticism because it did not recommend an outright ban on combustible materials in tall housing blocks.
"I simply fail to see how it is deemed appropriate for any combustible material to be used on any tower block in this country and I find it unfathomable that this review has not recommended an outright ban on the use of combustible material", he said on Twitter.
Hackitt said a new building regulations system should at first focus on buildings of 10 storeys or more.
He added: "We are consulting on significantly restricting or banning the use of desk-top studies to assess cladding systems".
The prime minister told MPs the work would cost an estimated £400million.
Mrs May had been criticised for her response to Grenfell tower fire, in Kensington, west London, which killed 71 people.
Shadow housing secretary John Healey said: 'More than 11 months on, the time for warm words is long past, and people are rightly asking why so little has changed since the Grenfell Tower fire.
Theresa May confirmed the risky materials would be removed during Prime Minister's Questions earlier today. David Lammy, the MP for Tottenham, described the report as a "betrayal and a whitewash".
Dame Judith will give now evidence on her report to the Housing, Communities and Local Government Select Committee at 3:30pm today.
But her decision not to advise a ban on combustible cladding or insulation for high-rise buildings drew immediate condemnation from a wide range of critics including the opposition Labour Party.
"If people feel I haven't gone far enough and for this system to work in the future requires, in addition, that there is further clarity or indeed banning of some of the materials which are now used, I don't have a problem with that", she said.
But the answer to the key question of whether the government should ban combustible materials, such as those which spread the flames on Grenfell where 72 people died, was left unclear.
The review found that some building firms use the ambiguity around the rules to "game the system", with the primary motivation to "do things as quickly and cheaply as possible" rather than focusing on quality.
She said the new regulatory framework must also address the fact that "residents often go unheard, even when safety issues are identified".
- Clearer roles and responsibilities throughout the design and construction process, as well as during a building's occupation.