But the Welsh Government's request to councils to conduct fire safety tests is voluntary.
"Ministers have said that the public inquiry might be expected to look at why this cladding had been fitted in different parts of the country over a long number of years, and I'm confirming that", he said.
The overwhelming majority of the buildings that have failed so far have been council-owned or social housing tower blocks.
Mrs May's call came as Cabinet was informed 95 samples of cladding from tower blocks in 32 English local authority areas have failed fire safety tests - amounting to 100 per cent of all samples submitted by councils.
The blocks are Milton Mount in Pound Hill (seven storeys), Platform in the town centre (eight storeys), Pegler Court (six storeys), Bloomery House in West Green (five storeys) and First Choice House in Northgate (six storeys).
Nine tower blocks in Wales over ten storeys are run by housing associations. All testing of those materials are "voluntary" for the private sector.
The crisis has now spread to the Scottish Parliament - MSPs were told last week Scotland's more stringent building controls banned plastic-filled cladding on high-rise accommodation.
He is among 18 victims to have been formally identified in the fire, the worst in London in decades; the British police have said the death toll is likely to rise.
Crystal Palace confirm appointment of Frank de Boer as new manager
De Boer had been linked with other jobs in England, while Palace have had plenty of changes in the dugout in recent years. We will look at one or two signings, but I think it is necessary to see all the players here first ".
Putin recalls Russian ambassador at center of Trump collusion investigation
His first tour of duty as an envoy to the United States was between 1985 and 1989, where he specialized in arms control. He commenced his role as Russian ambassador in Washington shortly before President Barack Obama was elected.
Everton 'beat Arsenal' to sign Nigeria attacker
Henry, who scored 22 goals in 38 games for Belgium's KAS Eupen last season, will, however, be loaned to Anderlecht next season. Onyekuru is expected to spend next season on loan at Anderlecht as he does not yet qualify for a work permit in the UK.
"CHC is working with members to ensure that every step is being taken to prevent anything similar happening in Wales and to reassure tenants".
"But now we have witnessed a catastrophic failure, on a scale many thought impossible in 21st-century Britain".
There are no tower blocks within Crawley - this term is used for buildings over 12 stories. 'What we can say is that the building is being evacuated for fire safety reasons and flammable material was found'.
Cardiff council, which has nine high-rise blocks of which several were over-clad in the 1990s, is now using an independent contractor to conduct a survey.
Responsibility for the fire safety of a building under law rests with the owner of the building. The survey will nclude an analysis of the make-up of materials used, and if anything is needed checking, samples will be sent for checking.
Labour housing spokesman and deputy leader, Councillor Ross Houston said: "It's right that the council is allocating resources to these works, so there is no delay in getting them done, but it can not be right to foist the cost onto tenants and leaseholders".
"The buildings are clad with traditional, fire retardant material".
The council will also review its fire safety policies following any recommendations from the Fire Service.