Can I set up a UK limited company if I live outside of the UK and if I’m not a UK national?

You can form a UK Limited company, even if you do not live in the UK or if you're a non-UK national

The director and shareholders can be of any nationality and live anywhere in the world. The director's will need to be at least 16 in order to be appointed an officer of the company. 

Your company however, will require a UK Registered Office address.