ISIS has claimed responsibility in a statement on its Amaq Agency:

“With Allah’s grace and support, a soldier of the Khilafah managed to place explosive devices in the midst of the gatherings of the Crusaders in the British city of Manchester, in revenge for Allah‘s religion, in an endeavour to terrorise the mushrikin, and in response to their transgressions against the lands of the Muslims. The explosive devices were detonated in the shameless concert arena, resulting in 30 Crusaders being killed and 70 others being wounded. And what comes next will be more severe on the worshippers of the Cross and their allies, by Allah’s permission. And all praise is due to Allah, Lord of the creation.”

Worth noting their numbers are significantly inflated and their claim to responsibility is unconfirmed.