I quickly found my grandfather's record at Wilton Road School in Hackney which added a few extra details to my picture of him.
While the records vary by school and some are more detailed than others because they were completed by the school they are likely reasonably reliable. The records include:Admission Date, Name, Parents’ names, Parents’ occupation, Address, Birth date, Age. This amount of detail minimizes the chance of mistakes.
I checked a page of the Westminster Jew´s Free School and noticed a column from the 1870s asking for Christian name duly completed. Remarks like "Gone to Work" and "Required at Home" were common, less then half the children completed the 6th year of schooling.