What are my chances of getting into Oxford university?

It's kind of Difficult to say what your chances are without more information about what the health problems were. Ignore what the first answerer said. Oxford and Cambridge DO take into account reasons why you haven't been able to fulfill your potential. If they believe you have the potential to score highly but have been stopped by outside circumstances such as family bereavement or illness, they're perfectly willing to offer you a place. I am at Cambridge University myself, and so I can't speak about exactly what Oxford will do in this case. At Cambridge, we have something called the special access scheme (well it was, it's now called something new, but the same thing) which is a scheme specifically for people who have the potential to succeed but have got low grades for reasons beyond their control. It involves filling in a few extra forms etc. Oxford don't have a formalised scheme like this, but they DO still consider your circumstances. I'd advise e-mailing an admissions tutor at Oxford (you can find contact information on the website) to ask about exactly what their process will be for assessing whether you do indeed have the potential, but have been blocked by your illness.

The department of Physics say "There are no formal requirements for performance at GCSE; the majority of successful candidates have between 4 and 9 A* grades at GCSE, but it is not unusual for candidates to be accepted with fewer than 4 A* grades, or to be rejected with more than 9 A* grades." However, be aware that although they say this, it would be quite rare. However, there would be no harm in applying, at least then you'll know, rather than wondering all of the time whether you would have got in.

The department of Physics say "There are no formal requirements for performance at GCSE; the majority of successful candidates have between 4 and 9 A* grades at GCSE, but it is not unusual for candidates to be accepted with fewer than 4 A* grades, or to be rejected with more than 9 A* grades." However, be aware that although they say this, it would be quite rare. However, there would be no harm in applying, at least then you'll know, rather than wondering all of the time whether you would have got in.