Council leader Marion Atkinson calls for tighter controls after police warn of firework misuse.
Thousands of visitors were expected to watch the displays which were scheduled over three nights.
A dispersal order is authorised after reports of "youths congregating and setting off fireworks".
Organisers say they still want to put on the events even though it gets harder to stage them.
The company had no licence to store the explosives in a barn and containers, which were destroyed.
It is the second year in a row that the event has been cancelled.
A fireworks display was cancelled after organisers said it could not be held safely within budget.
Two teenagers were arrested following incidents in County Tyrone.
The annual event held during the Blackpool Illuminations is set to start on Saturday.
