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The UK has two basic types of school: taxpayer-funded, free-to-attend schools called ‘state’ schools and fee-charging schools which are known as ‘private’ or sometimes, possibly just to confuse Americans, ‘public’ schools. As far as I can tell there’s no canon information on where the BBC versions of either Sherlock or Watson went to school (ETA: untrue! see: comment thread about John's CV). So fanficcers have to fill in the gaps.
Primary schools
To the age of 11, kids will be at a state primary, or more rarely at a ‘prep school’ – i.e. a private junior school. Almost all primary schools are day pupil-only, and the state ones seldom have much of an academic focus. Prep schools however often do – a child genius popping up in the ranks will be the focus of a great deal of attention as they are basically walking capital: they are sure to win a bunch of scholarships at secondary school application time, which provides the school with a prime lure for wealthy parents who are looking for somewhere that will brain up their intellectually indifferent offspring.
An exceptionally bright kid appearing in the state system would be likely to attract formal assessment by a state educational psychologist, but not necessarily be subjected to pressure as a result. There are up sides and down sides to that: a genius in the state primary system is likely to be extremely bored, but also free to pursue their own interests a lot of the time. At a private school, it’s more likely that earnest attempts will be made to keep them interested, which can either be a blessing or a curse depending on the competence of the adults involved.
A child in the state system who demonstrates an IQ score above about 140 is unlikely to actually stay in the state system for much longer, assuming their parents are not actively hostile to private education or so poor that they can’t afford uniforms etc. after a 100% scholarship. If the child has not yet completed primary education, they are likely to be offered bursaries by prep schools eager to have their forthcoming secondary-entrance scholarship results to put up on the wall and impress rich parents with.
It’s also worth noting at this point that the state system, in my county at least, did have something called an ‘unteachables unit’. The psychologist’s report on me concluded that one option was to send me to this mysterious place, which apparently had a total of five other students, all there for less desirable reasons than the one I presented with. If Sherlock got sent there, as I can well imagine happening to a child who was neuroatypical along with being exceptionally bright, I suspect this can only have aggravated some of his more problematic tendencies.
State secondary schools
There are more varieties now, but in the 80s there were two types of state secondary school, comprehensives – which take everyone, as you might expect – and grammar schools. Grammars are feted as having been the route out of poverty for a lot of successful people, but they’ve also come under fire for being ‘elitist’ and have now been mostly phased out (though there are a few left). In the 80s though, most big towns had one. To get in, you passed the '11+' entrance exam (which Sherlock could have done in his sleep). Anyone can apply, you just have to want to do it and have parents who are supportive enough to let you.
I spent two-and-a-half years at a state grammar, and basically enjoyed it. The place was academically focused without being pressurised; everyone around you was at least moderately brainy, and if you were so bright as to baffle people then you were at least left alone and sometimes even respected. On the other hand I didn’t have any friends as I still found the other kids on the thick side (or I was screwed up and had no social skills, another way of looking at it).
If a kid opted out of the 11+ or wasn’t put up for it by hostile/uninterested parents, then they went to a comprehensive. Unfortunately even a very good comprehensive is not likely to lay on a programme of study engaging enough to prevent an adolescent genius from, basically, deciding that it’s far more fun to fuck shit up, and a lot of them are not good. ‘Bog-standard comprehensive’ is a politically notorious phrase with some grounding in fact. Sherlock at a comprehensive is likely to find drugs, profitable crime and the independent study of illicit subjects to be far more interesting than the curriculum. (ETA: comprehensives do stream for ability, though I don't know anything about this. See ununpentium's comment on LJ.
Private secondary schools
Most private secondary schools are day only, many are day and boarding and a few are boarding only. The boarding ones in particular lay on an extensive range of extras and activities, including before and after school sports/clubs, Saturday lessons and Sunday services and activities, which the day children may or may not have to attend. Sixth formers at an academically-focused private school are usually permanently exhausted and sleep deprived because it’s not actually possible to fit the volume of work in any other way. On the other hand, private schools have longer holidays.
In in my experience and that of friends who’ve undergone the same process, sending your child ‘genius’ to boarding school is little short of torture. Particularly before the age of 13, the philosophy of the schools I attended was to knock all individuality out of their charges in the name of healthy adjustment to communal life, and at least in the late 80s the gold standard for healthy adjustment was a Lord of the Flies common denominator of herd behaviour. If you want to imagine your way into it, start by positing that you are under 24/7 observation in a room with a dozen juvenile thugs. You have to your name one bed, one shelf and one locker, the contents of which are routinely plundered and vandalised, and any protest to authority results in you being told that it’s all your fault for not trying to fit in.
I was, somewhat incredibly, sent to boarding school to ‘make me more normal’. The state psychologist believed I’d undergo some kind of socialisation process, and my parents didn’t know any better than to believe him. If anything like this happened to Sherlock… well, I suspect he didn’t like it. I’ve inflicted it on him in fic (Points of Light), if only in the form of flashbacks.
For kids from rich families, boarding school can be slightly less appalling – they know what the experience is like, but it’s regarded as a necessary hard-boiling process. And the child involved will probably suffer a bit less because of having a home support system, parents who will be listened to by the school authorities, and possibly siblings to lean on as well.
My personal money would be on the BBC Holmeses having come from a rich family of high achievers – the accent, silly Christian names, demeanour and galloping sense of entitlement all point to it – and gone to a private boarding school (Eton, Harrow and Winchester are the most prestigious options for boys). At a stretch they might have gone to a state grammar and then polished up their accents at Oxbridge. But Mycroft in particular is proceeding to the top of his career exactly like a man with the demons of a public boarding school education snapping at his arse. I know people who are doing this IRL.
What are ‘genius’ kids like?
There are a few recurrent themes apparent among the people I went to school with.
Crushing insecurity with a flip-side of arrogance is an almost inevitable side effect of the whole experience. I can certainly be accused of this. Because your sense of what’s normal was set at a time when you could do everything that came your way as a matter of course, as an adult if there is anything that you can’t do with thoughtless ease, you feel you are an utter failure. Adult Sherlock may have remained genuinely exceptional in his own field in a way that most high-achieving kids don’t, but he also treats things he can’t do with such sneering contempt that you’ve got to figure it’s the galloping insecurity coming through, right there.
News stories like this one make me wince. At first it's fun being singled out like that - all the grown-ups make such a fuss of you. But as you get older and less cute, certain adults become hostile and defensive. And even once you've grown up yourself, you're carrying the weight of unmeetable expectations. The burden can come to define you.
Alienation from family is a particular difficulty for kids who have been gifted brains by a genetic quirk rather than as part of a family trend. Worst case scenario, a kid from a modest background goes away to boarding school and comes back fucked-up, piled with books and spouting in an upper-crust accent to baffled and resentful family members who wonder where their amusing little human encyclopedia has got to, because he used to be so cute, and why the hell does he want to study Ancient Sumerian poetry at university when with his brains he could do maths then come back to his home town, marry a nice girl and get a respectable job that would make his parents proud.
Mental illness is another thing that quite a lot of teenagers seem to acquire without needing an exceptional IQ, but if you have spare brains they will help you to cover up and/or feed your neuroses. I aced my GCSEs while suffering from undiagnosed bipolar, and had the presence of mind to be able to attempt suicide, wake up, go home, behave normally and explain away the resulting physical marks. Sometimes, if you are that bored, in a way mental illness is something to do. You get to stay in your own so-much-more-interesting-than-everyone-else’s head, which is your favourite place even if all the contents have lately gone black and started to gibber. I suspect the concealment and denial stops working if you have a psychotic break, however.
This raises interesting questions about Sherlock’s much-discussed diagnoses. If he has some kind of full-fledged neuroatypicality like autism, then he probably did show the resulting oddities in his youth. If he just suffers from a selection of neuroses of the depression/disordered eating/hates-everyone-for-existing variety, then he would have been quite capable of showing authorities only the picture he wanted to show.
Genuinely eidetic memory (lack thereof): I certainly don’t have one, and IRL I don’t know anyone who has. You don’t necessarily get one just because you’re bright, and Sherlock’s is good evidence for his neuroatypicality. I am in awe of people with eidetic recall. Awe!
Regression to the mean: Genius kids don’t always grow up into genius adults. Research suggests that a kid scoring 130 Stanford-Binet will turn into an adult scoring 120, or a score of 160 will likewise reduce to 140. A genuine excess of brainpower seems to behave like other kinds of juvenile excess: eventually you get over it and settle down into someone who has, let's say, tendencies, but isn't defined by them. This happened to me (which can be interpreted as either healthy integration into society or a crushing failure) but it clearly didn’t happen to Sherlock. Which makes him an exception squared.
Some fascinating further reading on Perspectives on intelligence in Sherlock