Could? Yeah, definitely. Should? It probably depends on your temperament. If you are going to do it, there are classes you can go to, as well as online courses you can take that will help you learn the course material. I personally really don’t recommend self-study; you are talking two years with very little in the way of outside positive reinforcement to keep you on the right path, and you have to find the will to study consistently by yourself for two years. I tried several times to self-study A-levels, and they all failed, partially because they are designed for students still in school, and less about those outside of school. The courses are still possible, but it will be much harder now that you have to think about paying bills and the like on top of studying.
If I had decided to go to classes to do A-levels, I probably would have been ok. That being said, I did an access course, having previously determined myself to not do one, and it was the best choice I could have made. I kind of wish I had done my A-levels now, but seeing as my goal, like yours, was to go to a good university, I don’t regret this too much. An access course isn’t as much of a defeat as I originally thought, and you should consider why you don’t want to do one, in order to find what works best for you with studying; this will also help you with finding the right uni and degree. Good luck!