What we are doing in stepping back into the Middle Ages with Lewis’s guidance is attempting to challenge that “line of immediatism” in two ways:
First, from the 17th c. to today, the primary religious authority of scripture/tradition has increasingly given way to that of reason/experience. To desire to learn from the cloud of witnesses or “church triumphant” – those one whose shoulders we stand – is to shift authority back to the older style, weighting Scripture-read-through-tradition more heavily than the dictates of individual reason and experience.
Second, from the 17th c to today, the primary way individuals have met God has shifted from a church-mediated to an individual, unmediated mode. Any full and useful appropriation of the past—that is, one not content just to offer doctrinal direction—will likely seek to return to some form of churchly mediation, whether of liturgical forms, priestly role, or both, attempting to reverse this post-Enlightenment trajectory.
Look, feel, and results of immediatism
What, then, does immediatism look like in evangelical churches today, and how does that degrade our ability to gain benefit from the church of the past?
The narrative of (individual) desire
David Bebbington famously defined evangelicalism with a fourfold typology: Biblicist (the Bible as the ultimate authority on all matters of faith and practice), crucicentrist (the atonement secured for us by Jesus on the cross as the central reality of our faith), conversionist (a “born again” crisis experience as necessary and definitive for the faith of each believer), and activist (the tasks of evangelizing individuals and reforming churches and societies as imperative on all believers).
I suppose that when we talk about evangelical immediatism we are talking about something like Bebbington’s “conversionism”—but that category by itself is inadequate to describe the habitus of affective devotion and unmediated communion so central to this movement. To understand the continued impact of immediatism in evangelical faith, we need to expand Bebbington’s “conversionism” to include a focus on personal relationship with God in Christ, not only accessed (immediately, in several senses) through a crisis conversion experience but also experienced in a continuing way through a series of direct, affectively powerful, transforming encounters with God.
Again, in order to fully take into account the impact of immediatism on evangelicalism, we would also have to understand that evangelical “biblicism” has taken on a similarly direct, un-mediated character: through reading the Bible as individuals, apart (as the movement has falsely imagined) from any communal or traditional filters, we have clear and immediate access to the mind of God.
We are shaped by the stories we tell ourselves. The ruling reality of evangelicalism is unmediated access to God. As the twentieth-century ambassador of Pentecostalism David Du Plessis put it, “God has no grandchildren.” That is—no individual and no generation may claim faith based on their forebears (which is after all, in a sense, the claim of all tradition!), but all must meet God for themselves.
The pragmatic shape of church
Now, how does this look in our churches?
Structurally, evangelical immediatism is inherently individualistic and impatient of organizational structures and constraints. It has therefore created a kind of “hole in the ecclesiological donut”—where everything that inhabits the realm between the mystical communion of the “church invisible” and the immediate communion of the individual with God is negotiable and, ultimately, a matter of adiaphora (that is, these mediating forms are considered inessential for salvation).
Yes, the local church has often played a strong role in the lives of evangelicals, but one might argue that its primary role is not to mediate, but to celebrate and foster the individual’s immediate communion with God.
In other words, as historian Bruce Hindmarsh argues, the evangelical movement has always represented “an unparalleled subordination of church order to evangelical piety.” Thus almost all inherited forms—all the practical, ecclesiastical wisdom of the early and medieval church, for instance—have been negotiable. (This has been true notwithstanding the tradition-oriented tendency of evangelicalism’s Anglican parent, which much of evangelicalism has inherited, to center Christian identity in the forms of corporate worship.)
This allergy to churchly mediation has given evangelical churches a decided lean toward democratic, participatory forms of worship and leadership. Congregationalism has been the movement’s favored leadership form, and worship styles have tended to follow whatever seems to relate most naturally and directly to the worshiper. This has meant preaching in plain language and singing in popular styles (famously, even tavern tunes!); if God meets people immediately where they are, then people should use in worship whatever contemporary popular-culture material already feels natural and “homey” to them.
So far, three things to note
First, affect (“heart religion”) drives immediatism.
Second, immediatism drives pragmatic, plastic ecclesiology.
Third, ecclesiastical authority is a subspecies of mediation, so immediatism seems best served by “flat” forms of organization.
 David W. Bebbington, Evangelicalism in Modern Britain: A History from the 1730s to the 1980s (London: Unwin Hyman, 1989), 2-17. Related to this observation is the important secondary one that Bebbington’s “crucicentrism” (cross-centeredness) is not currently universal among evangelicals—particularly if one includes Pentecostal groups, which still account for a hefty percentage of members in the National Association of Evangelicals. Among many of these, “pneumocentrism” (Spirit-centeredness, so to speak) has often replaced crucicentrism to a great degree. And as we have seen, Pentecostal (or charismatic) styles of worship have deeply influenced much of modern white evangelicalism since the 1970s, so this is not a minor point.
 Bruce Hindmarsh, “Is Evangelical Ecclesiology an Oxymoron? A Historical Perspective,” John G. Stackhouse, ed. Evangelical Ecclesiology: Illusion or Reality (Grand Rapids: Baker Academic, 2003), 15-38.
 Hindmarsh, “Is Evangelical Ecclesiology an Oxymoron?” 15.
 Evangelical Anglican J. I. Packer has argued, in his “Stunted Ecclesiology?” (J. I. Packer, “A Stunted Ecclesiology?” in Ancient & Postmodern Christianity: Paleo-Orthodoxy in the 21st Century—Essays in Honor of Thomas C. Oden, ed. Kenneth Tanner & Christopher A. Hall [Downers Grove: InterVarsity Press, 2002]) that evangelicals are not as stunted in theory in their ecclesiology as is often said, though they may fail to come up to the theory in practice. An interesting footnote: the Anglican communion shares their centering in worship with Eastern Orthodoxy, which seems to make a bridge across which a few young evangelicals in the 20th and 21st centuries have felt comfortable walking—right into Orthodoxy. According to some Wesley scholars, this affinity is not without substance or precedent, as Wesley is supposed to have been influenced deeply by certain Eastern fathers.