Actually I was baptised in an independent church, and which used Anglican liturgy, believed in some dispensationalist ideas and practiced infant baptism while being very vaguely English Baptist in worship style. I believe it may hev also from time to time had Methodist Preachers. It was however, quite clearly, not in any sense, what Americans would call 'non-denominational'.
As far as I can see non-denominational is a 'movement' of independent churches, not formally affiliated, but which share a broad trend of worship and theology, and are in effect if not actually on paper a denomination, in that a person from one non-denominational church will probably feel more at home in another n-d church than in say a Catholic cathedral, a Mennonite Church, a Quaker meeting hall or a Greek Orthodox Church, which one might expect, but also more at home in another non-denominational than in a Methodist, Baptist, Pentecostalist or Adventist Church.
I may well be wrong I usally am.
cj x