The samples were submitted after the massive fire at Grenfell Tower earlier this month, which claimed at least 79 lives and displaced hundreds, and also led to an announcement of a public inquiry.
The latest "major investigation" is expected to fall under a second phase of that inquiry after all cladding samples submitted by local councils failed the testing criteria.
"That remains a 100 per cent failure rate," May's official spokesperson told reporters at Downing Street.
It is believed that all the tests so far have involved local authority owned blocks in the UK, rather than private buildings.
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Samples of cladding were also being sought from schools and hospitals, but it is not yet known whether any had been tested.
"It must identify each and every individual and organisation who must bear responsibility and accountability for this tragedy and the mishandling of the aftermath. There must be swift recommendations to ensure there can be no chance of a repeat of this disaster elsewhere," reads the letter signed by the Justice4Grenfell campaign.
The Grenfell Tower blaze, believed to have started in a fridge-freezer, destroyed 151 homes in the north Kensington block and in the surrounding area of the London Borough of Kensington and Chelsea.
Meanwhile, the US firm that supplied cladding used on Grenfell Tower says it has ended global sales of the product for use in high-rise blocks.
Arconic said on Monday that it was discontinuing sales of Reynobond PE for tower blocks due to "issues" identified by the fire.