If it is assumed that the Inklings can be characterized as more than the sum of their parts, and more than a shared essence; then Owen Barfield may be regarded as the philosopher of the Inklings, and Tolkien as the supreme practical exponent; Lewis as the mediator and Williams as the initiator and guide.
Despite that these individuals disagree - we can synthesize from various of their elements a group-identity from selected and complementary aspects of each; a group-identity which is not an average, and not shared by all of them, and to which none of them as individuals would subscribe.
Whether we do this or not is entirely a matter of what use or value we find in such an idea - working (as we should) in the broader context of the Inklings core and shared and universal ideal value - which was indeed Christianity.
(Christianity defined in some simple, basic and 'minimal' sense.)
Taken in this spirit - the Inklings have an intellectual lineage (via Barfield) which links them with Romanticism - especially Coleridge and Goethe; as transmitted via Rudolf Steiner and Owen Barfield himself. In other words, a focus on Imagination as the primary mode of thinking.
And furthermore, this lineage is forward-looking and not reactionary. I mean, this lineage does not look back to an ideal of immersive 'Original Participation' (rather like the un-self-conscious living in nature of Bombadil, the Ents, Silvan Elves, or to some extent the Hobbits) - but forward to an as yet only partially glimpsed and achieved Final Participation.
As a first example to consider: The Lord of the Rings - in terms of the deeply-appreciative reader's engagement with the book - takes its place in this tradition as being a supreme example of Final Participation (albeit temporary and partial).
So, instead of regarding LotR as in itself a yearning for the past and embodying a vision of history as a long decline and defeat; we instead regard it in terms of how we think LotR - how the book works in our thinking as an objective reality.
And because the objective reality of LotR is one which we cannot take 'literally' (it is a feigned history) we then experience it as fully-imaginable, fully-real; a mode of thinking that is more-satisfying-complete-and-imaginable-than-mundane-life (we cannot, or at least do not, appreciate workaday life in the modern world as fully imaginable - hence it does not seem fully real) - yet a reality that we simultaneously 'know' is essentially and substantially a consequence of our own minds.
We imagine, and we know we imagine, and this imagination is very-highly engaging: we participate in it.
So, although Tolkien rejected Barfield's anthroposophy; and although Barfield did not personally enjoy or appreciate the Lord of the Rings, the tow can be formed into a complementary structure which expresses some distinctive to 'The Inklings' - yet which is apparent only in retrospect and to those who were not themselves Inklings.
I am far from saying this is the only or best way to consider The Inklings - but it seems a legitimate, coherent, and potentially very fruitful line of enquiry.