There was no immediate claim of responsibility, but Chief Constable Ian Hopkins said police are treating the blast as an act of terrorism "until we know otherwise".
Manchester police have arrested a 23-year-old man in relation to an terrorist attack at an arena that killed 22 people, many of them children, after a concert by United States singer Ariana Grande.
Jeremy Corbyn has said this was "the most awful and traumatic time" as "there can be nothing worse than losing a child in a situation like this".
Many Manchester residents responded early Tuesday with offers of shelter and details on locations where displaced concert-goers had been taken in. "Let us remember those who died".
Finance minister Philip Hammond said: "It is as far as we know a terrorist incident".
Speaking outside her 10 Downing Street official residence, Ms May said the authorities were not ready to announce the identity of the attacker. It has been reported that the remaining dates will be cancelled in the wake of the attack, but this has not been confirmed.
Police were called to reports of an explosion at the Manchester Arena at 10.33pm, shortly after USA singer Ariana Grande had finished her performance.
Eyewitnesses described the scene of metal nuts and bolts among the debris and fear and confusion amongst the concertgoers.
More than 400 officers were deployed on the operation throughout Monday night.
Armed police work at Manchester Arena.
Meanwhile anyone who witnesses suspicious activity is urged to report it to the anti-terrorist hotline.
The first to be identified was Georgina Callander, an 18-year-old Ariana Grande fan who once met the singer. "And if there turn out to be others responsible, to seek them out and bring them to justice". An 8-year-old girl was among the dead.
"I seen people running and screaming towards one direction and then many were turning around to run back the other way".
While NHS Blood and Transplant (NHSBT) said it has enough blood to treat victims at present, it urged people with upcoming appointments to follow through with them - particularly if they were blood group O negative.
Nana Julie Mills said: "Just heard one of my good friends whom I've known since he was a little boy passed away last night".
She said her thoughts are with the victims and the families of those who have been affected.
Scores of gun-toting police - a rare sight in Britain - were patrolling the area and the nearby Victoria railway station, near the explosion site, was closed down.
"So many young, beautiful, innocent people living and enjoying their lives murdered by evil losers", Trump said during a visit to Bethlehem.
Manchester bombing: Missing people. "The incident took place outside the venue in a public space".
"Our thoughts and prayers go out to the victims", it said.
Shortly after May made her statement, The Queen spoke of her shock in a message to the Lord Lieutenant of Greater Manchester.
According to police the lone male attacker, detonated a homemade bomb killing himself as well.
"We continue to liaise with the United Kingdom authorities in response to this incident".
Emergency services at Manchester Arena.