It is not true that all independent schools have significantly longer schools days.
DD goes to an independent primary and is going to an independent high school. They are typical of all the independent schools locally, infact her primary has slightly longer days than the norm even for the local independents :
Infants: 8:30am to 3:30pm
Juniors: 8:30am to 3:45pm
Secondary: 8:30am to 3:30pm
They have a longer lunch time and have two breaks each day (morning and afternoon) where most of our local state juniors and secondaries only have a morning break.
They have 3 extra week's holidays - a week extra at Christmas, Easter and the summer.
The finish at noon before each of these holidays. They usually break up on a Thursday, and they always return back on the Tuesday. They have half to a full day off a year for scholarship day - to celebrate the Y6s getting scholarships into the high schools.
DD's primary school never closes for snow as small enough to cope on skeleton staff. The other independents DO close on snow days, regularly.
There is NO weekend school.
The after school clubs and homework clubs are all optional.
The breakfast is optional.
They do have smaller classes. Rather than paying for teaching and support staff to open longer and longer - why not plough the money into more staff to enable this is state schools instead?