I do not have a BSc, but a BA. Can I apply?
Yes. However, you should be aware that cognitive neuroscience is an experimental science and without a basic scientific grounding (e.g. statistics, experimental design) you are likely to be at a disadvantage. You will need to be able to demonstrate competence in these areas (e.g. by taking a top-up course) and a clear commitment to the subject (e.g. to have already undertaken wide reading). You need to have the ability, knowledge and skills to successfully complete the MSc.