Are there any medical issues that could stop you joining up? What's your plan if you aren't successful in applying to the Navy? If it's a career where you need a degree I would advise finishing your studies so you have a fallback plan.
Also, do you have enough examples of responsibility to demonstrate your leadership potential at interview? Would staying at uni and joining one of the uniformed organisations, helping with societies, doing sports or volunteering be of benefit?
A part-time degree is doable, but youve gog 30 weeks of basic training, then it very much depends on the professional training and your role as to how much time you'll have to dedicate to it.
Speaking as an ex-RAF Recruitment Officer.