Hey!! Your very welcome!! Yes, your careers advisor is right, and you should definitely do some work experience and super-curriculars as Universities love this. It will also be beneficial for you as well in the long-run as they provide great opportunities and experiences for all.
Regarding AS Further Maths, I believe that you should look on the websites of the Universities that you are interested in and look at their A-Level Grades and Requirements, don't pick your subjects based on what people tell you. This is a very COMMON MISTAKE!! Remember it is YOUR A-Levels, so I suggest that you do your research so you can feel comfortable in knowing what you will choose and gain a better understanding of the subjects that are required so you have an idea of what to choose.
Definitely read books related to Computer Science, do research, and perhaps, look at different websites about Computers Science. I know this isn't linked to your A-Levels, but I would like to give some advice based on picking your University. Make sure you that pick a degree and University based on what you would enjoy and feel comfortable learning. For example, if the Computer Science degree course for Durrham, you didn't like the topics/curriculum, and for Oxford you did, then I would suggest that you look more into Oxford, because you would not want to spend 3 years doing something you do not enjoy!!
WOW THAT WAS LONG!! Hope this has helped, and have a nice day!!

