Traditional Baptist churches "separated" from a church organization that was "top down" with the hierarchy dictating doctrine, and formed churches that were autonomous, adhering to doctrines consistent with their understanding of scripture. Also, along this line, were folks who thought the originating organization could be fixed, purified, and "reformed," but the "traditional Baptists" thought the originating organization could not be fixed, and they needed to fully separate from those dictating top down doctrine. Thus the "English Dissenters View" of the origin of "traditional baptists" is the one modern scholars hold.
Here is a blurb from Wikipedia:
Baptist churches have their origins with John Smyth, Thomas Helwys, and John Murton in the Kingdom of England and the Dutch Republic.[14][15][16] Because they shared beliefs with the Congregationalists, they went into exile in 1608 with other believers who held the same positions.[17] They believe that the Bible is to be the primary guide and that credobaptism is what the Bible teaches.[18] In 1609, the year considered to be the foundation of the Baptist tradition, these exiled Dissenters baptized believers and their church became the first Baptist church.[19][20]
John Smyth was a "puritan" but after being excommunicated from the Church of England, embraced "believer's baptism" and rejected "infant baptism."
John Smyth's church which relocated to Amsterdam due to persecution of dissenters under James I. In 1609, the church began practicing believer's baptism, and in 1611, part of the congregation, led by Thomas Helwys, returned to England and founded the first Baptist Church on English soil in Spitalfields, London. John Murton became the pastor of the church after Helwys died in prison in 1616.
Their legacy is comprised of our traditional baptist distinctives, which advocates full religious liberty and Soul Liberty and Separation of Church and State. Also note that General Atonement, Christ dying for all mankind, provides the "liberty" for any lost person to obtain salvation by grace through faith.
On the other side of the ledger are those that believe in top down polity, where leaders dictate confessions and creeds which must be accepted or the person lacks "saving faith."