passports – return trip from the UK to a non-EU country

I am a Ukrainian citizen and I live permanently in the UK with permission to stay for an indefinite period. The United Kingdom is my permanent place of residence and my place of work. I have never owned an adult passport, but I want to go to Ukraine to visit my family and come back to the UK.

If I get a Ukrainian passport, will I be able to return to the UK without applying for a visa? How it works? Do I need some sort of document to return to the UK?