In the UK it used to be that one traditionally studied for the A-level qualifications from the age of 16 to the age of 18. So, you spent two years studying, say, three A-levels (say, Maths, Physics, Chemistry).
Around 2000 it changed so that now the first year of study was called 'AS level' and the second, final year, called 'A2 level'. Together, an AS and an A2 in, say, mathematics, make up the mathematics A-level (GCE) qualification.
This was done to make the first year of study into a qualification in its own right. This offered more choice to students: you did not have to commit to a subject for two years, and end up with nothing if you left after one year. Plus, you could e.g. do AS levels in maths, physics, chemistry in year one, then the A2 part for maths and physics in your second year, but drop chemistry and pick up an AS in biology. Now you leave with A-levels in maths and physics, and AS levels in chemistry and biology. Under the old system, you would not have been allowed to study biology in your second year, and not have gotten a chemistry qualification for your one year of work.
What this means for you: you CANNOT use (say) AS level physics and AS level mathematics and present this as equivalent to one whole A-level. The two AS levels are still two years' worth of work, but they are not, for your website quote, considered as one A-level. [Imagine you studied at university for three years, but each year you swapped subject and started again - is this equivalent to a full, three-year degree in the same subject? Not really.]
So: to get an A-level in ANY subject, you must complete two parts - the AS level (first year topics) and the A2 level (second year topics). So, yes, you WILL need to take AS level exams (and then A2 exams) in order to get an A-level.