Unlike Grenfell Tower the block does contain modern safety features including a sprinkler system, wet risers fireman's lift and smoke evacuation valves.
Hundreds of residents hastily packed their bags and sought emergency shelter, with many angry and confused about the chaotic situation. Some refused to leave.
The testing is being done as officials around Britain scramble to assess the safety of apartment buildings following the June 14 inferno that engulfed Grenfell Tower in west London, killing an estimated 79 people.
Mrs May said the Government was working with local authorities across the country to address fire safety concerns about tower blocks following the Grenfell Tower tragedy. It said about 650 apartments were evacuated, though initial reports put the figure at 800 apartments.
"This means that we need to move residents from their homes and into temporary accommodation".
"We were told by London Fire Brigade that it wasn't safe to stay in four Chalcots blocks - Grenfell changes everything, and we had to act fast", Camden Council Leader Georgia Gould said.
Fiona McCormack from the London police said that tiles and insulation on the outside of the building "don't pass any safety tests".
In response, Jeremy Corbyn, leader of the opposition Labour Party, said May needed to "get a grip" and lead a stronger response to what is now a "national threat".
Residents complained of first hearing about the evacuation from the media and getting very short notice to leave from city officials going door-to-door.
Several local councils said they were removing cladding from the facades of buildings that had failed the tests.
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'I've sat in a chair over there since nine o'clock last night, I'm 72 years old, suffer with emphysema, and they can't rehouse me because I've got a dog.
"At 8:30pm (1930GMT) yesterday they told us: "you have to leave", I don't understand why", Murtaza Taha, 27, told AFP. "There's no organization and it's chaos", she added.
Carl McDowell, 31, said he took one look at the inflatable beds at the gym and went back to his Taplow apartment to sleep there overnight.
Last week, it emerged that Grenfell contractors had used a more flammable type of material for the outer layer of the cladding, which Philip Hammond, the Chancellor, said was banned in Britain.
Earlier Friday, police said they were considering filing manslaughter charges in the Grenfell disaster.
The Metropolitan Police said cladding attached to the 24-storey public housing project during a recent renovation failed safety tests conducted by investigators, and they had seized documents from a number of organisations.
McCormack said police were investigating companies involved in the building and refurbishment of the tower, and possible "health and safety and fire safety offences".
Meanwhile the government ordered immediate checks on the Hotpoint FF175BP fridge freezer model blamed for the blaze.
Hotpoint said it was working with authorities to examine the appliance, adding "words can not express our sorrow at this bad tragedy".
The Department for Communities and Local Government (DCLG) later confirmed that the polyethylene filling between the two Reynobond aluminium panels did not pass building regulations for tower blocks over 59 feet and a flame retardant material should have been used instead.
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