Deputy director of children's services Cecilia Hitchen, team manager Gillie Christou and Maria Ward, the social worker in charge of Baby P's case, have lodged the appeal with the council.
If they fail to be reinstated it could pave the way for the three to take their case to an employment tribunal.
A Haringey council spokeswoman confirmed that all three former employees have lodged an appeal with the local authority.
All three were dismissed late last month amid allegations they had failed to protect 17-month-old Baby P, whose name has now been revealed to be Peter.
Hitchen was dismissed by a panel of councillors due to alleged "loss of trust and confidence", while Ward and Christou were sacked for alleged gross misconduct.
It is not yet known whether Clive Preece, who was sacked from his role as head of safeguarding at the same time, also for alleged gross misconduct relating to the case, will appeal.
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