Mandy Pinney and Hayley James had the last ceremony of the day and were escorted behind the curtain to say a final goodbye to their father Terry James. They later received a fine for overrunning by the council who owned the facility.
A spokesman for the council said the complaint would be looked into.
The statement from the North East Lincolnshire Council said: “As the policy stands, a charge is imposed on the funeral director if a service at the crematorium overruns. Funeral directors manage the proceedings and it is at their discretion whether or not to pass this charge to their client.”
Philip Spicksley, executive chairman, AOIC, said: “Clearly there is always a balance to be struck between allowing time for grieving relatives to say goodbye and ensuring the smooth running of a crematorium.
“It is the job of professionals, whether they are the celebrant or minister conducting the service, the funeral director or those managing the crematorium, to find that right balance, or indeed be guided in the right way. If North East Lincolnshire Council is looking to provide guidelines that clear up any possible confusion and ease distress for families then it must be welcomed.”
An FOI request also found that, six families have been charged extra for running over by less than two minutes, with 20 fines issued over a 21 month period costing £4,000.