The statement of action should be prepared within 10 working days of the final inspection report. It will, of course, take longer than that for the school to come out of notice to improve or special measures.
The article Rosebud05 links to is itself somewhat confused (as is the letter from Michael Rosen she linked to on another thread which, amongst many other howlers, implies that it is harder to find out which academies are on notice to improve or in special measures than it is for non-academies). Let me start with the situation for non-academies.
Ofsted can place a school on notice to improve or put it into special measures. No-one else has that responsibility. The school will remain on notice to improve/in special measures until Ofsted say otherwise.
If parents have a complaint and are unhappy with the response they receive from the school they can take that complaint to the LA.
The LA can issue a formal warning notice to any school if they feel that, although it is not performing poorly enough to be considered inadequate by Ofsted, it is nevertheless performing poorly in relation to its intake, past results or similar schools. They can also issue a warning notice if they consider there is a threat to pupil safety. Obviously it is possible for a warning notice to be triggered as a result of complaints from parents. The Secretary of State can require an LA to issue a formal warning notice to a school.
Looking at academies:
Ofsted can place an academy on notice to improve or put it into special measures. No-one else has that responsibility. The academy will remain on notice to improve/in special measures until Ofsted say otherwise.
If parents have a complaint and are unhappy with the response they receive from the academy they can take the complaint to the EFA. It appears that at least some staff at EFA are not aware of this. That is clearly a problem that needs to be resolved.
The Secretary of State can issue a formal warning notice to any academy. Obviously it is possible for a warning notice to be triggered as a result of complaints from parents.