Chuck at Occidentalist assembles a bunch of test reports, here and here. It's not a well-studied subject as in the U.S., so it's hard to make sense of all the data. I haven't seen a good meta-analyses by a British researcher who knows the ins and outs of all these acronyms like GCSE. (For example, a few years ago a British researcher slipped up on writing about regional differences in performance on the SAT in the U.S. because he didn't know that only the most ambitious students in the Midwest take the SAT instead of the ACT.) But most of the data seems to suggest a smaller cognitive and/or achievement gap in the U.K. than in the U.S.
It has been apparent for some time now (see this post at Racial Reality) that in Britain, the lads are not all right. In the U.S., we've become familiar with gender gaps on school achievement tests favoring black and Hispanic girls over their brothers, but we see less of this among whites and Asians. This is among the better evidence that culture — fear of being put down by your co-ethnics for Acting White, etc. — is depressing NAM performance.
On a lot of tests, in Britain, there's even a bigger gender gap favoring the distaff side, but it seems to go across all ethnicities, even Chinese. We see weird things like girls whose parents are from Africa outscoring white boys and maybe even East Asian boys on some tests.
As I pointed out in a couple of articles in 2005, class is the big divide in Britain than race. "Class" is a 1500-year-long project to civilize the Conan the Barbarian warlords who inundated the Roman Empire to act like "gentlemen." By the late 20th Century, all that politeness, all that studying, all that self-discipline, was striking young males of the lower classes as pretty gay. Thus, chavism.
In contrast, there isn't all that much of an oppositional culture among blacks in Britain, since assimilating into the white working class isn't terribly hard: You like 'aving a pint while watching footer on the telly, too? The proportion of mixed race children appears much larger than in the U.S. As historian David Starkey pointed out during the English looting last summer, that blacks were in the lead, but whites were right behind — something you don't see in the U.S much at all.
Moreover, blacks in Britain are of immigrant origin: West Indian and African, with the Africans doing better on tests, typically. Some not insignificant fraction of Africans in Britain were brain-drained from Anglophone ex-colonies to work in National Health as nurses and doctors. In the U.S., West Indians and African immigrants tend to outperform native blacks. The Bell Curve found that in the NLSY79 longitudinal study, blacks who were immigrants or the children of immigrants outscored native African-Americans by an average of 5 IQ points.
But, those are just a few speculations. It's an interesting question that, as far as I know, hasn't been studied terribly systematically.