Edith ofsted have no involvement in the private sector
"A few examples of behaviour:
'Taking a book to circle time'
(to which my response would be "was he told to put the book back? and if so how did he respond? if not why did you not address the behavior at the time rather than flag it as a potential behavioral problem?" Presumably the nursery have a rule that circle time is when children sit quietly on the carpet, and while they may not want the children to bring books, the issue is more about how he responded to being told to put the book back rather than the fact he brought it in the first place.
'Refusing to let another boy play with him in the "shop"'
("Was this a one off behavior? and if so how was it addressed at the time and how did he respond to being told to share?")
'Screwing up his work'
(erm, work?
ok, well my response to that would be "was this a one off or is it a regular occurrence. How has he responded to being told not to do so in future?")
'Crayoning on the carpet'
(again, a one off or regular occurrence, and what response to being told not to? Can)
'Squeezing another boys cheeks'
("Was the other boy physically hurt? and if so why was I not informed at the time?")
'Being slow to put on plimsols'
(hahahahahahahahahahahahahahaha.I've spent considerable amounts of time in reception and y1 classes, and that is just so normal that it doesn't even warrant a response to them IMO. In fact my ds is nine and would never get dressed in time if I didn't constantly shout encourage him to do so..)
'Being "all over the place" in the afternoon when tired'
(the key here is that he is only three and is tired. This is normal.)
'Playing by on his own - alongside others rather than with them'
(is this a constant or something that is intermittent? Because all children should be able to play by themselves, the key is whether they can interact with others.)
'The teacher mentioned that he "gets the blame" for things which are not his fault. I nearly cried at this point.'
(gets the blame from whom? The teacher? or the other children? And if the other children, what is being done to correct their misassumptions?)
Tbh op I would get him the hell out of there and move him to another and more nurturing nursery. And I would let hell freeze over before paying the probably extortionate fees to have him in that school. If this is what their nursery environment is like, the school will only be worse.