The firefighters are said to have allowed the youngsters aboard the off-duty engine during an open day at the Greater Manchester Fire and Rescue Service (GMFRS).
Senior figures at Manchester's Fire and Rescue Service said they have had words with employees who backed the party, saying it was a cause for 'concern'.
Crews from Greater Manchester, Staffordshire and Shropshire Fire and Rescue Service worked together to control the fire that started at around 6.30am on Checkley Lane near Bridgemere.
Crew Commander Pete Langton was sacked by Buckinghamshire Fire and Rescue Service for making 'misogynistic and sexist' comments about the woman after pulling her from a blaze.