Seafront operators of inflatables were found to hold the appropriate safety certificate during inspections carried out after a three-year-old girl's death, a council has said.
Ava-May Littleboy died when she was thrown from an inflatable trampoline in Gorleston, Norfolk on Sunday.
Four firms running bouncy inflatables in neighbouring Great Yarmouth have been visited by inspectors.
Great Yarmouth Borough Council said all four supplied the relevant evidence.
They were asked to provide public liability insurance for the year and their Pertexa Inflatable Play Accreditation (PIPA) certification, which ensures an inflatable conforms to safety standards.
A council spokeswoman said if evidence was not supplied, the local authority reserved the right to exercise the terms of their operating licence, which could mean asking them to cease to trade.
Companies trading or hiring inflatables in Great Yarmouth have been asked to provide the equivalent evidence.
"Notwithstanding that, it is the operators' responsibility to ensure their equipment is safe," the spokeswoman added.
The company which ran the trampoline - which witnesses described as exploding - was the sole operator in Gorleston and is not currently operating.
Witnesses described how people tried to catch Ava-May, from Somersham in Suffolk, who had been at the beach with her family.
A post-mortem examination found she died of head injuries.
Earlier this week, Harlow MP Robert Halfon called for the temporary ban of inflatables in public areas until they are found to be safe.
It followed Ava-May's death and that of seven-year-old Summer Grant, of Norwich, who was inside a bouncy castle when it was blown several hundred metres in Harlow in 2016.
On Wednesday, a Hampshire council said it had imposed its own ban until the inquiry into Ava-May's death was over.