True enough -- they broke off from the Puritans who broke off from the Anglicans who broke off from Rome.
The English Baptists did break off from the Anglicans, who broke from Rome. But they aren't the only Baptists. Furthermore, most individuals today who are Baptists, were never part of the Romish church. AND most Baptist churches today, in 2011, came into being totally apart from any influence or involvement from Rome.