A spokesman for Prime Minister said she was “deeply saddened” by the incident which has claimed the lives of at least six people already, with many more injured.
With questions already being asked as to the responsibility of both local and national government, Ms May ordered the gathering this afternoon.
A Number 10 spokesman said: “The Prime Minister is deeply saddened by the tragic loss of life in the Grenfell Tower and is being kept constantly updated on the situation.
“She has asked for a cross-Government meeting at the Civil Contingencies Secretariat to take place at 4pm to co-ordinate the response and ensure the Government is ready to assist the emergency services and local authorities as necessary.”
He added: “The PM’s thoughts are with all of those affected by this terrible incident and the emergency services, who are working tirelessly in very difficult circumstances.”
Hundreds of firefighters were sent to 24-storey Grenfell Tower in north Kensington, as large plumes of smoke billowed above the capital after the blaze broke out in the early hours of Wednesday morning.
Witnesses spoke of “terrifying” scenes, with some residents suggesting they heard no alarm go off when the fire began. At least 30 people have been taken to five hospitals and six are confirmed dead.
It has already emerged that Ms May’s new chief of staff, Gavin Barwell, had failed as housing minister to carry out a fire safety review of tower blocks, despite the recommendation to deliver one being years overdue.
A fire expert behind the report calling for the desperately needed safety appraisal, said he had spoken to Mr Barwell earlier this year and the then-minister told him he was “still looking at it”.
Mr Khan condemned the "bad advice" given to residents of the West London tower block that was engulfed in flames overnight, killing several inhabitants and leaving many trapped inside the burning building.
A newsletter to residents in 2014 said the "stay put" policy worked because the block had been designed according to “rigorous fire safety standards”.
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