"Many, many Christian churches have no liturgy. Many of them have "Bible" in their name.
"
If those churches have an order of worship that they follow, then they have a liturgy. Maybe there is a freeform church somewhere, but I've never seen one. What would the service be in such a church? I'd be very interested in finding such a church so I could visit it. It would be unique in my experience.
If you find a church called, "(something) Bible Chapel," chances are they will follow the Plymouth Brethren tradition where the Remembrance meeting, a.k.a. the Breaking of Bread meeting, is free-form.
I believe that the Friends (aka Quakers) have "free-form" meetings.
I have never attended one, but my understanding is that the worshipers sit in a reverent silence, and whenever an individual feels led to speak to the group, or pray aloud, they rise and do so at any time.
I don't believe they have any liturgy or any type of structured service.
If there are any Friends on this thread, perhaps they can clarify or correct me if I'm wrong :)