I didn't do any work over the summer, and was just fine. However, if you feel like you want to get ahead, then do it! I read ahead maybe once in my Yr 12 and the next lesson I felt very smug as I knew everything. It did make the lesson quite boring, though, as I was only going over stuff I'd already learnt.
tl;dr: It's not a requirement, so you don't have to.
As for first year, I didn't find the content a step up as much the amount of content and the difficulty of exams. I was told that I'd drop two grades going from GCSE to A-level and was prepared for that, but honestly if you managed to just glide through your GCSEs (as I did), it's more like "you will drop to a U and you have to fight for every grade upwards".
Overall, the main advice I can give is get your revision technique correct early, and stay on top of your work. If you can manage them both, there's very little reason to not get good grades at the end of your AS levels.