If you can find a part-time, BPS accredited conversion course and your employer is happy to let you work part-time, then you absolutely can still work while doing your degree.
The quickest way is a bit tricky. Neuropsychologists are specialised clinical psychologist. To become a clinical psychologist, you need to do a DClinPsy, which is extremely competitive and three years long. In order to get into the DClinPsy, you will ideally need a lot of experience - in this instance, you being a RMN will work wonders for you, although they'll probably want something else as well. There is also a debate on whether having a masters or not helps...