The 'Sixth Form' thing is complicated. When I was at school (many years ago now!) the first year at secondary school was called the first year, during which you would normally turn 12, then 2nd, 3rd, 4th & 5th years followed, with O levels (now replaced by GCSEs) being taken in the fifth year. After that you could leave or go on to the 6th form, which was divided into the Lower Sixth (16-17) and Upper Sixth (17-18) and you would normally take your A levels in the Upper Sixth - there were no AS exams as there are now.
When schools started to count school years from primary level, the 'first year' became Year 7, 'second year' Year 8 etc - but many schools continued (and still do) to call the last 2 years 'the sixth form', while others call it Year 12 & Year 13. (And incidentally the sixth form college DD is at always refers to its students as being 'First Years' or 'Second Years')
In some areas all schools have their own sixth form, in some none do, and A levels are taken either at a Sixth Form College or at a college of further education. Some areas have a mixed system, with some schools ending after Year 11 & others having a sixth form.
To complicate matters further, you don't have to do A levels at all if you want to stay in education post-16 - you can do National vocational qualifications (NVQs) which are 'work-related, competence-based qualifications', or various other diplomas and qualifications.
Finally, I know of at least one institution that calls itself a University (Thames Valley University) which admits students from the age of 16 to do AS & A levels NVQs and various diplomas, certificates and Awards!
Hope this helps