The basic difference in the UK is that what Americans think of as "graduation requirements" must all be completed by the 10th grade. Kids who are on what we would think of as a "trade school" trajectory can leave high school at that point, once they pass their GCSE examinations. Everything in the UK equivalent of 11th and 12th grade is strictly directed at college prep, and is normally further directed at a planned college course of study.
There are plenty of situations where a kid who was hoping to go to a school like Imperial College (a very selective Engineering/Medical school) might take 3-4 math classes in their final two years of high school; they just would not be likely to be taking any English or History classes at the same time.
The UK and Irish systems drop any pretense of generalist education after 10th grade, and they always have reserved the upper levels of high school for the college-bound -- in fact, in my parents' day, the cut-off in the Irish system was 8th grade. I was always having to fend off well-meaning social workers who wanted to give my parents information on GED classes when I was in school, after those surveys we used to have to fill out that asked about family education levels, which always phrased it as "number of years of schooling completed." My parents did have their HS diplomas; they just got them after 8th grade. They both went to trade schools after that: my mother studied tailoring and my dad was a master cabinetmaker.
PS: For our interested UK teachers, the calculator DS was required to have for 7th grade was a TI-30X Scientific Calculator, at around $20 (
http://www.officedepot.com/a/products/176928/Texas-Instruments-TI-30X-IIS-Solar/). Starting in 9th grade, he'll be required to have a TI-84+, at around $100 (
http://www.officedepot.com/a/products/208377/Texas-Instruments-TI-84-Plus-Silver/). As a pp noted, there are some schools that supply the calculators on a deposit system, but in most places it is more common to require each student to purchase their own. Since they have to be used for exams, they normally cannot share them. However, it should be noted that by no means all schools in the US require this level of math; there are many, many districts where the TI-30X would be the most advanced calculator you would ever need.