The boy was swept out to sea on Friday night after he and five other boys and a girl, all aged 15, went to play on a concrete ramp. They ignored safety chains and signs warning people to keep off.
Two of the boys were also swept off their feet as they tried to help the 13-year-old, but managed to scramble clear. A man dived into the sea in an attempt to reach him but was beaten back by the waves. A passer-by threw a lifebelt but this failed to reach the boy.
A search involving lifeboats and helicopters continued until 2am. A shore search resumed after dawn, only to be called off temporarily as the tide rose again.
Earlier, the teenagers had disobeyed two social workers who gave them permission only to go to the funfair unsupervised. They were on a day trip from a Rochdale residential home.
Rochdale's director of social services, Ian Davey, said: 'Everyone concerned is shocked . . . obviously I will be mounting a full investigation to see just how this accident happened.'