I think we can all agree that there is a huge differential in schools in England. While the A level exams are the same for everyone, pupils' experience in the years leading up to them can be radically different, and can be affected by a range of factors. These include school life (school expectations, quality of teaching, whether you are taught by subject specialists, peer group pressure, behavioural issues, amount of school support etc) and home life (home environment, supportiveness of parent towards education, caring responsibilities, need for a part-time job etc). This is one reason that universities use contextual information when making offers.
To a large extent these differences are ironed out at university where for 3 (or 4) years students have the same access to lectures, to tutors, to resources such as libraries and laboratories, to student support and so on as anyone else on their course. They are also mostly free of the disadvantages of a disruptive/chaotic home environment. So to that extent degrees are a 'fairer' reflection of a student's true academic ability.
The style of teaching, and of learning, at university is markedly different from school – it's much more independent and self-reliant, which will favour some students over others, and not necessarily those who did best at school. University also allows students to focus in on an area of study which really interests them, and there may be quite a number who are not all-rounders but are very, very good at one specific subject. Such students will benefit from a university education.
A levels are obviously one marker of ability at 18, but they don't actually tell you very much about 21-22 year old graduates. Interestingly, when you apply for a Masters, most universities do not ask for your A level grades, which I think tells you how universities themselves view the relevance of A levels once you have a degree.