If you are on a US base or linked you might have access to a US school on base, useful if you are only going to be here a couple of years.
If you are looking at state schools, well catchents ae quite loose these days so you will be looking for where has a place as these are in year admissions.
Virtually every UK school has a uniform, some stricter than others, the rules vary between schools and can be down right daft.
Your 11 year old will be in secondary school (high school).
Do you know how long you will be in the UK? The main school exams are taken at age 16 and are called GCSEs, students normally take 8-10 subjects and these are roughly, very roughly equivalent to a high school diploma and accepted by US universities.
To get into a UK university you need two further years study either at A Level or BTEC, A levels are taken in 3 or 4 subjects, BTEC level 3 is a selection of units in a single broad subject.
So the big difference is that UK schools specialise early, the GCSE course work starts in year 9, or year 10 at the latest, the grade depends, for most subjects, on a final exam taken in May or June of year 11, some have some course work but this only counts for a small % of the final grade.
Re the church going, the only subject that is compulsory in English schools is RE, and the law says schools need to have an act of 'daily worship' this varies between schools, some basically ignore the law on worship, others (usually RC or other faith schools) take it more seriously.
Both your children will learn about Christianity and at least one other faith, most schools do a wide look at world regions.
IN the UK it is not common to ask people what church they attend, we tend to think that's a private business, there is a saying that having a faith is like having a penis, it's fine to have one, but it isn't polite to wave it around in public.
and that the first floor really means the second floor not the ground floor like it does here
No the US is wrong on this one, the rest of the world has a ground, first, second etc.
Some words to watch out for, 'fanny' is not your butt, it is a vagina, fanny packs are bum bags.
A rubber is an eraser, don't be surprised if your younger child asks you if you have one.
What we call chips are what you call fries, what you call chips are crisps.
A bang has a number of meanings, one sexual, if your hair is in bangs it is a fringe.
Suspenders are ladies underwear, braces are what hold trousers up.
If you order coffee or tea it will have milk in it unless you ask for 'black' coffee or tea. BTW Betty's tearooms is a must for a decent cuppa.