Both sets of players had agreed that the English League Southern Conference game should go ahead after inspecting the Alexandra Palace rink before the face-off.
Peterborough complained to officials, however, after one of their players sustained a groin injury on an uneven section of the ice when they were trailing 4-1. Players protested that they could feel concrete under their skates.
The rink was being played on for the first time since it was used as a dressing-room for the MTV Europe Music Awards two weeks ago.
The Haringey manager, Dave Loudfoot, said: "The ice was relaid last Sunday and all of my players were happy to continue. I have seen matches played on ice much worse than that.''
He added that he would appeal to the English Ice Hockey Association to award his side the victory, and would agree to a rematch only if the game restarted from the second period with Haringey's lead intact and identical teams.