Hi! I'm in my final year of studying Neuroscience at King's College London. Here are a few thoughts that I would have liked to know before starting my degree.
Shirel.barda is right that there's a mix of careers you can go into, and I would add in maybe consulting, public/ global health policy making, science communications (for companies, or for publications/magazines) or working in the NHS as a clinical scientist (NHS-STP). However, be aware that a lot of these will require Masters or Doctorate level qualifications for you to be competitive. The common theme however, is that they're all related to the bioscience/life science industry. You could also leave biosciences entirely and go into finance/econ, the civil service, or teaching - but there may be easier ways of getting into these industries than with neuro.
Academia is a tough one to get into, and a tougher career to sustain yourself through. You'll need a PhD, and then it's 5-10 years of post-doctoral study before you can take up a lectureship position somewhere. It is a very very long grind. And only then do you start the journey towards being a professor - all the while trying to compete for the very limited amount of funding that universities/institutions have. I'm not going to lie it's a long road and you aren't particularly well paid for it either, so only go into academia if you really really like it. I know it might suck a little to hear this, but it's better to find out before going into it than finding out later like me haha.