I don't know. That hasn't come up in the story yet.
I was about to ask the same question. You need to know before you start writing about the school because they are very different. Brits will be able to tell it's a private or state school even if the topic of fees/money never comes up, and also will know if the writer has confused the two and is just relying on hearsay and stereotypes.
Also as they're 11, are they at primary or secondary school? If they have only just turned 11 they'll be in year 6 and the oldest kids in primary school. If they're turning 12 later in the school year they'll be in year 7 and at secondary school and the youngest kids in the school. This makes a massive difference to the school as primary and secondary schools are very different.
All my answers are from a state school perspective as I went to state school. And it's based on England (you said your school's definitely in England... Welsh schools are an entirely different kettle of fish. Many of them teach in Welsh, for starters...) And I'm a parent and used to be a teacher so I know how things are in schools now compared to how they used to be.
In primary school they'll have one teacher who teaches all or nearly all their subjects, which may include PE too. They may occasionally have lessons with specialist teachers (this could be PE). They will spend most of the day in the same classroom with their class teacher. PE would be done in the PE hall - or school hall if it's a small school - or on the field. In the hall is much more likely in January as primary school teachers tend to be a bit gentler and kinder about making kids go running around in the rain. Plus they'll be coming back to their classroom soaking wet (as opposed to secondary school where they'll be making some other teacher's classroom soaking wet). Even if it's not raining, the pitch will be very muddy.
In secondary school they will have each lesson in a different classroom (or specialist room like a science lab for science and the school field or sports hall for PE) with a specialist teacher and there will be a school bell (or buzzer or similar) indicating when each lesson ends. As they're year 7s and it's only January (start of the 2nd term), this will be new to them and still feel like quite a big deal, though they should know their way around well enough by January to not get lost.
Your character won't be allowed to not participate in PE. It's compulsory. You'd need a medical reason to not participate and some schools will require a doctors letter to verify this, as there's often a problem with parents allowing kids to skive PE by writing letters asking for them to be excused over trivial things. This is more of a problem in secondary school than primary school.
School PE tries to be inclusive so children with long term medical conditions or disabilities will be included in PE, i.e. expected to participate albeit with modifications to the activities. Many state schools will include children with disabilities right across the curriculum.
Type of activity: any sport or exercise activity would be fine as PE is a lot more varied nowadays compared to how it used to be. Certain things like having "boys" sports and "girls" sports is frowned upon (and against discrimination laws), and it's frowned upon to just offer traditional team sports like rugby and football (soccer). Secondary schools usually can offer a wider range of activities however primary schools with specialist PE teachers may still be able to offer a wide range. The PE curriculum will include exercise activities that aren't sport or competitive, e.g. dance, aerobics, circuit training. Activities like gymnastics are usually done in a non-competitive way. If they've got the equipment they'll also include things like trampolining and table tennis. Athletics is more often done in the summer and rugby is more often done in winter (injuries are more likely when the ground's hard) cricket, tennis, baseball and rounders tend to be summer sports. Football, (field) hockey and netball are more often done in winter. Indoor sports may be done in winter if the weather's really bad. Most schools have an indoor sports hall as well as pitches etc. When I was at school indoor PE and outdoor PE were timetabled separately and you went outdoors regardless of the weather but that depends on the school. Also, unless the PE teacher is specially trained to teach rugby, rugby will be non-contact (tag rugby - instead of tackling you pull a tag off your opponent.) That is the same for primary and secondary schools, though secondary schools are more likely to have at least one PE teacher who can teach full contact rugby. Also England Rugby has rules about what contact can be done at what age so that's another thing to research if you choose for them to be doing rugby in school PE.
If you wanted a scenario where your character was watching from the sidelines while a friend participated in sports, then maybe the friend goes to an after school sports club. If there's a school team, they will train after school. Private schools tend to do much better than state schools at running school teams, though some state schools have good school teams at some sports. After school sports clubs won't just be for the selected team. Inclusion is considered more important than sporting excellence in state schools and often there aren't enough numbers to be that choosy about who's in the school team - it may be a case of having to actively recruit more players just to have enough to make a complete team.