Around 600 high rises across England are using similar cladding to Grenfell Tower, says Downing Street.
Tower blocks across the UK are being examined after the London blaze, which left 79 people dead or missing, presumed dead.
Three samples have been shown to be "combustible" and more results will be made public in the next 48 hours.
A No 10 spokeswoman said it was a "matter of absolute urgency" to tell residents.
Theresa May said all local authorities responsible for the flats had been told.
The announcement comes after the boss of Kensington and Chelsea Council resigned after criticism of the London authority's response.
Speaking in the Commons, Mrs May said that the council "couldn't cope" in the aftermath of the fire, and that it "was right" its chief executive, Nicholas Holgate, had stepped down.
- London fire: Who are the victims?
- Visual guide to the Grenfell Tower fire
- Flats acquired for Grenfell fire survivors
The PM said all UK councils affected were working with local fire services and "taking all possible steps to ensure buildings are safe and [to] inform affected residents."
After being pressed in the Commons for more details on whether the cladding passed fire and building regulations, she said the material tests are expected to be made public in the next two days.
Sajid Javid, the Secretary for Local Government, will give more details about the testing later.
More than £700,000 has been paid out to survivors of the 14 June fire and Mrs May said she wanted to reassure them that no money would have to be repaid.
She also said resources would be available to everyone affected by the fire, regardless of their immigration status.
"I would like to reassure people that we will not use this tragic incident as a reason to carry out immigration checks on those involved or on those providing information to identify victims or those assisting with the criminal investigation," said Mrs May.
"We will make sure that all victims, irrespective of their immigration status, will be able to access the services they need, including healthcare and accommodation."
'Nowhere to hide'
Replying to Mrs May's statement, Labour leader Jeremy Corbyn said Grenfell Tower residents were "let down - both in the immediate aftermath and so cruelly beforehand".
He said: "At least 79 people are dead - it is both a tragedy and an outrage because every single one of those deaths could and should have been avoided."
Mrs May said she expected to name the judge who will lead the inquiry within the next few days.
"We want to ensure when the judge takes charge, people feel they can have full confidence in the inquiry," she said.
"No stone will be left unturned. For any guilty parties there will be nowhere to hide."
- Council boss quits amid Grenfell criticism
- Sprinkler plan for tower blocks
- Trauma counselling for tower firefighters
Ex-Labour deputy leader Harriet Harman told Mrs May to "get a grip on this personally".
Six people died when a high rise - Lakanal House - caught fire in Ms Harman's constituency of Camberwell in 2009.
"The coroner in 2013 in Lakanal House said that those deaths were avoidable, that there should been sprinklers, that there should have been change in the fire instructions, that there should have been greater supervision of contracts and fire inspection," she said.
"[May May] said that [Grenfell] was an unimaginable tragedy and that those deaths should not have happened.
"They would not have happened if the government had acted on the Lakanal coroner's inquest rulings."
On Wednesday, the PM apologised for "state" failures following the Grenfell blaze. Later that day, Kensington and Chelsea Council confirmed that Mr Holgate was resigning.
In a statement, he said that Mr Javid had asked him to go, adding that his continued presence would be a "distraction".
However, a spokesman from Mr Javid's department said: "The appointment of chief executives is entirely the responsibility of the local authority."
The fire destroyed 151 homes - most in the tower block itself, but also a number of surrounding properties.
Mrs May said that 164 "suitable properties" had now been found for those made homeless, and they were in the process of being checked before residents can move in.
The new properties include a block of 68 flats in Kensington and Chelsea, sold to the government by the developer at cost price.
NHS England said that 10 patients across four London hospitals are still receiving care following the fire in West Kensington. Five of them are in critical care.
One of the hospitals which has looked after patients, King's College Hospital, confirmed it had treated three people with an antidote to cyanide poisoning.
However, the hospital has not yet confirmed if they were suffering from that poisoning - it said that giving the antidote may have been precautionary.
A study by the University of Central Lancashire has shown that hydrogen cyanide is produced when various building insulation materials catch fire, including the type used on Grenfell Tower.