There are a lot of church schools which are state-funded; how they're run is a matter of some considerable controversy at present (try Googling "Trojan Horse Birmingham" for an object lesson in what happens when Muslims try behaving like the battier end of the Church of England with regard to schools. Spoiler: it does not end well.)
One does not have to pay fees for state schools. "Free" schools are a sub-set of state schools and "free" relates not to their payment status but to their management structure, which in some cases appears to be the sort of thing which would cause a Bakuninite to go, "Good grief, this is just anarchy." One of the reasons for pushing "free" schools was to allow there to be a wider range of options for religious education - unfortunately, this came with all the problems you'd expect and a lot Michael Gove didn't.
Because of a variety of educational upheavals over the years*, you often find a situation where the "best" state school in a district (particularly at primary school level) is the one affiliated to a specific church, so you get all kinds of shennanigans and flip-floppery among parents anxious to make sure their sprogs get in there, including enrolling them in Sunday School and showing up conspicuously at Communion and so forth - in the brilliant BBC series Rev the relations between the local church school and the church (and between its headmistress and the vicar) is a recurrent plot point.
And then there are private schools which are fee-paying and are also affiliated with various religions. Previously they didn't have to follow the National Curriculum, but there's much more pressure on them these days, following some incidents which showed just how wacky religious education could get.
So it's not impossible that Patrick's at an RC state school, but for the reasons set out in other parts of the thread, it seems pretty unlikely.
*The current lot of changes were intended to "give parents more choice". Then the wrong sort of parents started exercising it, and all Hell broke loose.
Re: Peculiar O Level Timing
One does not have to pay fees for state schools. "Free" schools are a sub-set of state schools and "free" relates not to their payment status but to their management structure, which in some cases appears to be the sort of thing which would cause a Bakuninite to go, "Good grief, this is just anarchy." One of the reasons for pushing "free" schools was to allow there to be a wider range of options for religious education - unfortunately, this came with all the problems you'd expect and a lot Michael Gove didn't.
Because of a variety of educational upheavals over the years*, you often find a situation where the "best" state school in a district (particularly at primary school level) is the one affiliated to a specific church, so you get all kinds of shennanigans and flip-floppery among parents anxious to make sure their sprogs get in there, including enrolling them in Sunday School and showing up conspicuously at Communion and so forth - in the brilliant BBC series Rev the relations between the local church school and the church (and between its headmistress and the vicar) is a recurrent plot point.
And then there are private schools which are fee-paying and are also affiliated with various religions. Previously they didn't have to follow the National Curriculum, but there's much more pressure on them these days, following some incidents which showed just how wacky religious education could get.
So it's not impossible that Patrick's at an RC state school, but for the reasons set out in other parts of the thread, it seems pretty unlikely.
*The current lot of changes were intended to "give parents more choice". Then the wrong sort of parents started exercising it, and all Hell broke loose.