Sometimes people are confused about the "Church Of The Brethren" and what is known as "Plymouth Brethren". They are not the same. Actually, the PB is an open (more loose) fellowship division from the so-called "Brethren Movement of 1827". One can read some of the history around this movement on the site at www.biblecounsel.homestead.com
which avoids taking any name not given for all saints. It speaks of a revival of church truth out of the sectarian systems which were prevalent after the protestant reformation of circa 1500. The COB is not part of this.
In sequence, we can see true church history after the apostolic period, to have descended into a scattering of believers in Christ to homes, for secret readings and fellowship, to avoid the persecutions of the organized hierarchy of the RCC papacy. The RCC predominated with religious leaders who mixed Judaism with the Christian testimony and their own ordinances, and controlled all religious thought by force throughout the Middle Ages --- from about 500 A.D. to the 1500's.
Most people were illiterate at this time, and then a few educated priests from the RCC studied the holy Scriptures and began to teach that the RCC was in error ---and then had to run for their lives. This resulted in religious police seeking them out and much persecution (see Foxe's Book Of Martyrs). One of the principal voices among the disenchanted priests was Martin Luther, who was bold to post his 95 word thesis on the door of a prominent church building, essentially stating "justification by faith" and not by religious works. This, as most Christians know brought on the Protestant reformation movement. The believers who rallied to this opening of the Word of God became the various major denominations we know today. Of course, numerous other denoms. rose up following this independent trend, and it was primarily the gospel message of salvation of the soul.
In the early 1800's after the gospel message was thriving, God began to recover church truth as many saints were moved to leave the established and organized religious denominations seeking the meaning of the universal church. That is when the brethren movement was formed with such believers as Darby, Bellett, Wigram, Kelly, Mackintosh, who held to the Scripture and the truth of "one body in Christ".