How hard do I need to work to get into Oxbridge?

If I work hard, I appreciate that I will get good grades. However - how much harder do I need to work than my peers to get into a top university?
Academically, my educational career has not been perfect. I've maintained good grades and work ethic without having to do too much. My school is not in a great position, we have had many inconsistencies in KS3, particularly with the sciences. I may be smart for my school, but I fear that when I reach Sixth Form and ultimately, I will not be on par with those I want to be. I want to do as much as I can before Uni so that I am in a good position relative to others. How do I teach myself??

Oxbridge will look at where you went to school when they consider your application. Also, the A level grades are more important than the GCSE grades. Since, as you say, your secondary school had some problems, they will definitely look at that and take it into account. They will consider your grades in the context of your school's performance. So, if you are smart for your school, they will definitely see that you got the highest grades in your school etc and they will be impressed.
Yes, you need to work hard... the best Oxbridge applicant is someone who loves their subject, so much that they study it all the time, even outside of A levels, and can take a very high workload. The love for the subject is the most important part, but the "high workload" bit is very important as well. So yes, you will need to work hard, take 3-4 A levels, depending on what your sixth form offers.