Twenty-two people, including an eight-year-old girl, have been killed and 59 were injured in a suicide bombing at Manchester Arena, at the end of a concert by US singer Ariana Grande.
A man set off a homemade bomb in the foyer at 22:33 BST on Monday, in what Theresa May called a "sickening" act.
Armed police have arrested a 23-year-old man in Chorlton, south Manchester, in connection with the attack.
The Queen held a minute's silence at Buckingham Palace at 16:00 BST.
Two victims have been named so far.
Eight-year-old Saffie Rose Roussos was a pupil at Tarleton Primary School, in Lancashire.
Her head teacher, Chris Upton, said she had been "simply a beautiful little girl in every aspect of the word" and was "loved by everyone".
Student Georgina Callander, believed to have been 18, has also been named as among the dead.