I was going to tell you to go to Royal Holloway to do InfoSec MSc, because it's one of the best in the World. I came out from there a few years ago. But you are after BSc. So maybe you should aim to go there after BSc.

You can also do Sans.org's exams at the mean time, CCNA is good but only for networking.

Good luck whatever you decide to do.

Which type of Computer Security industry you are planning to get into? Different types means different skills requires to get in.