@sansary
I think it would have been reasonable for you to have expected a posting in response from one of the people here who post in favour of Whitehall Park School - no praise too great it seems, and also claim to be well informed about the school, for example by being on the PTA.
Rather tham meerly being a neighbour like me. However in default of better information, your question as to whether building operations will be finished by September 2018 seems reasonable, and I can give you my best guess.Then one of the people with a connection to WPS can come on, no doubt and say I am wrong...
The first point is that the site is divided into two halves. The half with the old School building on it, and the other half with the portacabins for the current puils on it.
The plan is to demolish the old School building and replace it with a new building. Once the new building is ready the children will move into it and the housing association will start building where the portocabins used to be. So the works finish when the houses completed.
So your question amounts to asking is there time for this to happen, before September 2018.
Well the Housing association say their build will take 18 months, although there could be delays. But let us assume 18 moths. Then for the building to stop by start September 2018, it needs to start 18 months before. Which is February 2017. So the school building needs to be ready for the children to move in to January 2017. (and the portocabins then removed which is a fast job) Now the contractors for the new school, extra space claim they can do the new build, on a cleared and prepared site, in seven months. This is seen as very optimistic by building professionals but thats the claim. That would mean that they need to have the site cleared (the old building completely demolished) and ready by end of May 2016.
I do not know how long they expect the demolition to take, it was supposed to start early December 2015, then, in early January, then in early February. As I write it has not started. Early March then?
Conclusion. Just about possible, but the timing tight. Assuming they start the demolition soon.