There was nothing in the Education Act 1944 (which controlled state education when your sister was at school) to say how the school year should be arranged. So, given that each local authority was free to determine their own holiday arrangements, it would have been legally possible for Nottingham City Council to operate a school year which ran alongside the calendar year.
However, having taken quite a bit of interest in the history of eduction in the UK (and particularly in Nottingham, as that was the source of the Newson studies into child development) I've never been aware of any such arrangement existing in the city.