I am sure Molio that you do realise that turning schools around is not all about grades! I speak as a former additional governor of a school that had 19% A-C Grades including English and Maths. Yes, it was one of the worst in the country.
The big problem is often the fact that quite a few teachers, and leadership, may well be very poor and will have to be moved on through capability, a difficult and very upsetting process. You tend to have massive problems recruiting good new staff (and never one from a grammar school) and very often the balance between trying to improve poor teaching over a period of time and going with supply staff is difficult to judge and not having enough staff is very common. The morale is usually very, very low in poor schools. The self esteem of the staff and pupils needs a huge amount of input. Frequently teachers are not assessing the pupils sufficiently well to plan their lessons, hence poor progress of many children, (especially of the higher achieving ones). Frequently behaviour and attendance are poor too. Often teachers do not follow the marking policy so feedback to the children is poor. Children are not given the best advice on future education. You often find failing schools do very little in terms of music, drama and competitive sport against other schools (I found that truly shocking) and there is an air of hopelessness. Senior management teams, when they are in place, will be continually monitoring the quality of teaching in the classrooms, going over every shred of evidence when tracking pupil progress, ensuring that the PP children are making as much progress as everyone else, and dealing with far more SEN, behavioural issues, social services cases, exclusions and general disruption, not to mention some vile parents than most MN contributors will ever imagine.
Believe me, you would not find this list at many grammar schools. However I know enough grammar schools to know the job of the Head is not easy in these schools because people have such high expectations and cruising is not good enough. Of course any new head of a high performing school has their work cut out to keep it there, but it is just not the same as turning around a failing school. I live in a selective county where the grammars are nearly all outstanding and the secondary moderns (not that they are now called that) have, over a period of many years, nearly all been in RI or worse, several times! Many of them are now better, but it is the grammars that are continually the best led. Lessons over - sorry if I have preached but it is something I feel very strongly about.