EDIT: This is the more organised and hopefully more useful post. Please ask questions! I will extend any of the sections if you like.
I am writing from a very very middle-class, white, professional background - which does seem to be the kind of background Hermione comes from. I'm also about the same age as Hermione, (a couple of years younger) so hopefully this will be helpful! However, please bear in mind that my experiences are not universal!
School structure
The overwhelming majority of children will attend a state school. These will either be entirely funded by the state, or receive some of it’s funding from a religious organisation if they are religious schools, e.g. Catholic, Church of England, Jewish etc.
Most children will attend a Primary School from 5-11 and then a Secondary School from 11-16 or 18. Some places have a Elementary/Middle/High School arrangement.
School Year
The school year starts in September, generally the first Tuesday of the month, with the Monday being a Teacher Training Day.
Autumn Term: September to December, usually breaking up the last Wednesday/Thursday before Christmas.
Autumn Half Term: Week long holiday, sometime in October.
Christmas Break: Two weeks.
Spring Term: January to Easter, usually the last Wednesday/Thursday before Easter.
Spring Half Term: Week long holiday, sometime in Feb/Mar (depending when Easter falls)
Easter Break: Two weeks.
Summer Term: End of Easter hols to mid July.
Summer Half Term: Week long holiday, usually May.
Summer Holiday: six weeks, from mid-July to last week in August.
School Structure
Infants
Reception – children turn 5 during the school year.
Key Stage OneYear One – children turn 6 during the school year.
Year Two – children turn 7 during the school year.
Juniors
Key Stage Two
Year Three – children turn 8 during the school year.
Year Four – children turn 9 during the school year.
Year Five – children turn 10 during the school year.
Year Six – children turn 11 during the school year.
Children will start school either the September before their fifth birthday, or the term before their fifth birthday, depending on the school/LEA policy. So a child born in October will always start in the September before their fifth birthday, but a child born in Februart will either start in the September before their fifth birthday or in the January before their fifth birthday.
Standard Assessment Tests (SATs)
Completed at the end of the Key Stages – so in Year Two and Year Six. Only in English, Maths and Science.
Awarded in levels:
Level One – below average for Year Two
Level Two – average for Year Two
Level Three – above average for Year Two/below average for Year Six
Level Four – average for Year Six
Level Five – above average for Year Six
Year six pupils can take an extension paper to see if they are working at a Level Six level, but this would normally only be done in schools where several pupils would take it.
A child should progress two levels from Year Two to Year Six. So a child who got an above average Level Three in Year Two would be expected to get a Level Five in Year Six.
Classes
Children stay in the same class for a year, and have one teacher for all subjects. It is quite unusual in British schools for children to be moved up a year and almost unheard of for them to be held back a year.
A School Day
8.30: Children start to arrive at school. Many will play in the playground.
8.50/9am: School starts, with a whole school assembly.
Morning Lessons: English and Maths
Morning Break: 15 minutes, around 10/10.30am.
Lunch: 12-1ish.
Afternoon Lessons: One or timetables activities.
Afternoon Break: Infants only.
3.15/3.30: Hometime.
Travelling to School
Many children live in walking distance of their Primary School, or short drive away. Some children will take a bus, but often this would just be a normal public transport bus, rather than a specific bus for school children.
Most children would be brought by a parent or other relative, but some arebrought by child minders or a friends parent. Older children may come on their own, perhaps with young siblings.
Teachers will be outside from about 8.30, 8.40. Some children may arrive earlier, but parents would be discouraged from this as there is no one to watch the children. Children will generally play outside until school starts, unless it is raining, when children may be allowed into their classroom.
Assemblies
Every day starts with a whole school assembly. All schools in England and Wales are required to have a daily act of Christian worship. An assembly would include the head teacher or other teacher reading a story with a moral lesson, normally linked to a teaching from the bible. There may also be announcements or awards, and everyone will sing a children’s hymn. Some schools have separate assemblies for the infants and juniors, but will still normally have one large school assembly once a week. (This may depend on the size of the school.)
Religious schools may replace the assembly with a special mass/service near religious occasions, for example at my Catholic school, the priest came and did a special mass near Easter and Christmas.
Lessons
Morning lessons will always be English and Maths. Each afternoon there would be one or two different subjects, including history, geography, art, music, P.E, science, design technology.
For example, Monday afternoon would be art and design technology, Tuesday would be history and geography, Wednesday would be science, etc, etc. I think P.E was once a week - maybe twice.
Breaks
All children get a 15 minute morning break and an hour for lunch. Infant classes would normally get an extra 15 minutes in the afternoon, and Reception classes may have longer breaks. Up until I was about 6/7 all children got free milk at morning break.
Lunch
Lunch is generally a packed lunch (sandwiches, yoghurt, fruit, crisps, chocolate) provided by the parents. Some schools did offer a cooked lunch, but in my experience even then the majority of children would take packed lunches. Children from poor families would get a free lunch - cooked if available, packed if not - provided by the Local Education Authority. Hermione probably wouldn't be anywhere near qualifying for this.
Packed lunches came in lunchboxes - brightly coloured plastic boxes with pictures of popular children's characters on them - like Power Rangers or Fireman Sam.
Uniforms
Uniforms are VERY common, even more so in primary school. Each school would have some colour associated with it. (Green, Blue, Red, Yellow. I haven't ever seen orange or purple. You would have different shades in different schools.)
A uniform would include:
white shirt
grey/black trousers or shorts for boys
grey/black shirt or pinafore dress for girls
tie in the school colour/design (might be plain or might be striped)
jumper in the school colour
a summer dress for girls, in the school colour and often checked
white socks
sensible black shoes
Recently (the past ten years) primary schools have been more relaxed, letting girls wear trousers, and generally swapping the shirt and tie for a white polo shirt. This won't apply for Hermione's time though.
Schools also have reading bags - these can be cloth or clear plastic, in which children take home reading books from school and a book to record that they have been reading with parents at home. Younger children probably wouldn't take anything else, but older children would almost certainly have a rucksack for carrying lunchbox, pencil case and homework to and from school.
Home Time
School finishes at 3.30. Children are collected by parents or other relatives, child minders or parent's friends. Older children might walk home alone, with younger brothers and sisters. Teacher will generally not let younger children leave without seeing their parent/appropriate guardian, but older children are given a bit more freedom, though there will be teachers outside making sure there are no problems.
After School clubs
In primary school these will depend entirely on the teachers at the school. So if there is a teacher who knows about football, there will be a football club, etc. Common afterschool clubs are: Choir, football and netball. More recently schools have started having gardening clubs, chess clubs, etc, but I don't remember these being very common when I was at school.
School Names
Religious schools maybe named after Saints, especially if they are attached to a church of the same name, e.g. St. Joesph, St Mary, etc. Schools maybe simply be named after the village/town they are, especially if they are the only one in the area, so Villagename Primary School, or after a local area, e.g. Green Park Primary School or Pretty Hills Primary School.