Using the info from John K I have found a transcript of the 1857 Act online for anyone who is interested.
This Act killed the original charter and statutes and set up the basis for the current operation. It was a Private Bill initiated by the Charity Commissioners. It had to be a Private Bill because they completely rewrote Alleyn's original scheme. I think there was a legal doctrine called cy-près which generally prevented diverging from the original terms - so the power of Parliament was required to re-write the Scheme.
Prior to 1857 the original statute was being used to provide some education for people living in Dulwich. In 1841 the Grammar School was opened (presumably the building on Gallery Road).
The 1857 Act killed this completely and gave authority for it to be closed. I think this Act also led to the closure of an infants school.
It appears there were two factions around the time of the 1857 Act - one faction wanted schools for poor scholars and the scheme to be used in that way, another faction wanted a great school to rival the like of Eton and Winchester. From the terms of the Act it seem clear which faction got their way.
I suspect most of this was prompted by the rapidly increasing wealth of the Dulwich Estate due to the arrival of the railways and from prior enclosing of common land.
As population grew the original scheme would have been very valuable to people living in the area covered. It is easy to see that today most of the funds of the Dulwich Estate would have been used for non-selective education of the inhabitants. Alleyn's original scheme did not provide for scholarships for pupils from outside the area, whom he called "foreigners".
It would appear that the 1857 Act would need to be amended by another Private Bill to reclaim more of the Estate funds for the general inhabitants.