E. H. Broadbent's book "The Pilgrim Church" presents a summary of Church history from the perspective of the local, quite often seperatist churches. These were known by many different names from: Montanists, Novations and Donatists; to Paulicians, Bogomiles, Albigensians, Cathar (pure), Poor men of Lyon, Waldensians and more recognizable; Lolards, Bohemians and Anabaptists.
They all rejected the church state (whether Orthodox or RC) as corrupt and attempted to restore the vision of pure, true christianity based on the Bible. They were persecuted left, right and center, sometimes in the case of the Anabaptists by Protestants and Catholics. The only one to survive from at least the early middle ages and possibly ancient times are the Waldensians, although there have been over 40 attempts to exterminate them.
This is the "Trail of the Blood" (see booklet by same name by J R Graves) of the true Church and although I don't think we can trace a continuous line back to the Apostles I think there is a true line of doctrinally (to lesser or greater extent, but more so than the state churches) and practically pure churches.
This is not to say that the Roman Catholic and Orthodox churches did not contain some true Christians and true biblical churches, just that it was much less clearly defined. Before the Reformation you could get away with a lot of veiws which, after the Council of Trent were veiwed as heresy. So before the Reformation the RC and the Orthodox churches were much less rigid. The major sin for them was that of the schismatics, like those listed above; for which the inquisition was developed after the Albigensian crusde, in the south of France, in the 12th century.
Those two books listed above ('the trail of the blood' is on the net, if you type it on google) and Miller's church history, provide interesting backgrounds to the evangelical underground, which I recommend you to research.
One interesting point as Vedder points out in "The Reformers and their Stepchildren and "An Anatomy of an Hybrid" is that it is the veiw of the Church put forth by the "heretics" listed above, which is most commonally held by Western Christians today; that of a believing Church, made up of voluntary participants, without the coercian of the state. Even the mainline Protestant state churches have adjusted their veiw to fit that of those they once persecuted.
Thanks for reading and I hope this has blessed you.