Most 16-year-olds take GCSE exams. (They replaced CSE and GCE O-Level exams, with the top CSE grade being equivalent to a basic pass at O-level).
AS-level examinations are available to 17-year-olds (i.e. after one year of '6th form' education). They used to count part way towards A-level results but they've now been 'decoupled' and function as 'standalone' qualifications.
A-level examinations are usually taken at the end of a two-year '6th form' course.
Those who go onto university normally study for three years for a Bachelor's degree, with those achieving the best results being awarded 'honours'. (i.e. candidates take a single set of examinations and can end up with or without honours, depending upon their results). At some universities though there are courses where candidates sit the examinations for a degree without honours one year and then go on to take the honours examinations a year later.
Bachelor's degrees are normally graded as follows (but there are some exceptions):
1st Class Honours
2.1 Honours
2.2 Honours
3rd Class Honours
Pass Degree
All Bachelor's degrees are 'equal in rank'. i.e. a BSc 'ranks' the same as a BA or BEd.
The highest achievers at that level can then go onto study for a further period (usually one year) for a Master's degree. (MA, MSc, etc).
Bachelor's degrees are always 'taught' degrees, where students learn from lecturers. Master's degrees are often 'taught' degrees but can sometimes be 'research' degrees (or a mixture of the two), where students carry out original research.
[Note: For historical reasons, those holding initial degrees (BA, BSc) from Oxford and Cambridge can 'upgrade' their Bachelor's degrees to Master's ones simply by paying a fee. So while MA(Oxon) or MSc(Cantab) might look like impressive qualifications, they're actually only 'initial' degrees that are equivalent to BA or BSc from any other universities]
The highest achievers can then remain at university to study for their doctorate. (PhD, DPhil, etc). With the exception of medicine, doctorates are always 'research' degrees.
Officially university degrees aren't 'qualifications'. They're actually 'classes of membership' of a university. (The Members of a University are neither its staff nor its current students. It's a university's alumni which comprise its membership). That's why universities are allowed to give honorary degrees to people who've never studied for them.