I'd say that the sort of maths taught at A Level is simply put not enough. It's taught in a very different way at university, there is an emphasis on proving things and exploring why concepts work, rather than just application. I think if you get an A at A2, you'll be on the same playing field as someone with an A* at A2, and they will also struggle with the mathematical demand of Computer Science if they don't put the work in.
If you want possible topics to do over the summer, I recommend you take a look at TheTrevTutor on YouTube, and start to get to grips with some of the discrete mathematics, or generally up your game on calculus, learn some of the stuff that isn't taught at A2, since as integrating something like xarctanx.
If you don't take Physics, then begin to start coming to terms with how circuits work, and some basic electronics stuff like combinatorial logic or sequential logic, which you can find on YouTube as well. You may or may not have access to your schools material for FP1/FP2/FP3, but if you do, it would be ideal for you to take a look at some of it, and attempt questions from there if it helps you to bridge from A2 to Computer Science level maths.
If you want to up your game on programming, I recommend you start to create mini programs in Java and C, as these are the languages used at the university, and this could make your life easier when you come here.
If you want to learn more about the theory behind computing, have a look at automatas and finite state automation, and start to explore different methods of how computers store things.
I'd say that if you haven't taken computing or D1, you should definitely take a look at the sorting algorithms, namely bubble sort, insertion sort, quick sort, merge sort, radix sort, lexicographic sort, timsort etc. You could look at greedy algorithms, dynamic programming, linear programming and even asymptotic analysis once your maths is up to scratch.
And if all that isn't to your liking, you could brush up your knowledge on web development, as there is an optional module you can take on it, and being able to produce a web application really fast would not hurt. You could also take a look at how the internet works, such as how HTTPS operates, and how the RSA algorithm is used.
This is all a variety of stuff which you're expected to know in the first year, so I'd aim to get to grips with all of it. I wouldn't let anything I've just said put you off this course, it is quite fun to learn about most of these things, albeit difficult. You'll be fine if you work hard