Nineteen people have been killed and more than 50 injured in a suspected terror attack at Manchester Arena.
Paramedics at the scene told the BBC they had treated some of the wounded for "shrapnel-like injuries".
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The prime minister has suspended Conservative Party general election campaigning and will chair a meeting of the government's emergency Cobra committee at around 09:00 BST, in response to the attack.
Mrs May said: "We are working to establish the full details" of what happened in Manchester. "All our thoughts are with the victims and the families of those who have been affected," Mrs May said.
BBC Home Affairs Correspondent Daniel Sandford said senior counter-terrorism officers were assembling in London and liaising with the Home Office.
Unconfirmed reports from two unnamed US officials suggested the attack was carried out by a suicide bomber.