Free Church ecclesiology is based on the development of three doctrinal presuppositions.
Firstly, the Scripture principle. In the realm of ecclesiology, the Scripture principle is taken to imply that there is a particular model for the organisation, government, and communal life of the church given in Scripture. This model, because it is Scriptural, is authoritative (mutatis mutandis, the church today should strive to be like the church then; some would omit the mutatis mutandis), sufficient (there is no need to look elsewhere for manuals of church order), and clear (the model is expressed simply and is easily understood). The particular model that we see in Scripture is church government by Elders and Deacons based in a local congregation, which is organised so as to express familial care and encourage gospel growth.
Secondly, the active rule of Christ by word and Spirit. Of course, every Christian accepts this presupposition. However, in Free Church ecclesiology it is developed in a particular direction. There is a tendency to reject any position of authority which is not based on the ministry of the word. Ministers are Christ's servants (again, Christians would universally accept this), but concretely that means that their authority is not their own; it comes through their service of the word. The authority of church leaders is the authority of the word; no exercise of authority which is not ministry of the word can be legitimate church leadership. A further implication is what might look like democratisation to the watching world, but is in fact an affirmation of Divine Monarchy. In other words, decisions are made by the congregation, under the guidance of the Elders, with the awareness that Christ is present and is exercising his rule. This also counts against complex structures in the church, and Free Church polity can look chaotic from the outside (and the inside!) - but it is based on the presupposition that Christ is actually ruling, and does not surrender his throne to, or share it with, any other human being.
Thirdly, the relationship between the invisible, catholic Church and the particular, local church. In essence, the former is thought of as manifested in the latter. Consequently, no room is found for structures over and above the local congregation. Such structures would either be attempting to manifest an 'interim layer' - not the catholic Church nor the local church - which would therefore be denying the identity between the one and the other; or they would be seeking to express the catholic Church visibly, which would be simple imperialism.
The more I think about it, the more these three principles and their implications boil down to one thing: Christ rules his Church, and therefore nobody else does. Of course, every Christian accepts, at least in principle, the first clause; the second is the particular genius of the Free Churches.