This is a helpful contribution to the discussion about Radical Orthodoxy. As a Catholic, I am in agreement with much (but not all) of the critiques presented here by the Catholic authors. James Hanvey's remarks about RO's misunderstanding of Barth are surely correct (see also the work by Kenneth Oakes). I do think that Conor Cunningham's book _Genealogy of Nihilism_ goes a long way to address some of Hanvey's concerns regarding analogy, however--not to mention Betz and Hart's work (two friends and fellow-travelers, if you will).
Regarding Hemming's essay, contra Pickstock his Aquinas scholarship is correct; however at almost every point his concluding remarks often miss the point. Hemming often engages in what Fr. Luigi Giussani would call a "reduction" of what Milbank and Pickstock are doing. I am in agreement with Hemming's thoughts regarding Milbank's unhelpful "evacuation" of philosophy for the sake of theology. I would argue that Cunningham's approach, both in his _Genealogy_ and his more recent _Darwin's Pious Idea_ reveal a more helpful Catholic approach where he is much more amenable to philosophy as "preparation" (cf. p. 85; and yes, I am biased here as Cunningham was my Doktorvater). For all of Hemming's focus on Aquinas, however, he--as well as so many other critics of RO--misses that Milbank's opening essay in _Radical Orthodoxy_ was not about Aquinas but J. G. Hamann, already an indicator of his own proposal of an "alternative modernity." Lastly, I would add that Hemming misses how analogy functions in Aquinas (see p. 90) as analogy itself functions "analogously", both in philosophy and theology (see Przywara and especially's John R. Betz's helpful interpretation of him both in the edited collection by Joseph White, OP and his introduction to his co-translated [with David Bentley Hart] edition of Przywara's _Analogia Entis_).
I do think that Hemming's initial essay (pp. 3-19) will continue to stand as an open question regarding the Anglican appeals to Catholic tradition. As a Catholic who himself is largely (though not completely) sympathetic with the task/sensibility of RO, I am not the target of this question, however.
In some ways, as Fergus Kerr's essay points out, much of the response to RO can be understood--even now--as the difference between 'concilium' and 'communio' Catholicism.