It is obvious why this would have appealed to McDiarmid. I'm surprised that Auden didn't include this poem in his light verse anthology; it was sufficiently well-known that either A. or the Doddses would almost certainly have read it, it meets the criteria, and the quoted passage is reminiscent of Auden's famous analysis of T.S. Eliot's sensibility:
I step into my heart and there I meet A god-almighty devil singing small, Who would like to shout and whistle in the street, And squelch the passers flat against the wall; If the whole world was a cake he had the power to take, He would take it, ask for more, and eat them all. And I meet a sort of simpleton beside, The kind that life is always giving beans; With thirty bob a week to keep a bride He fell in love and married in his teens: At thirty bob he stuck; but he knows it isn't luck: He knows the seas are deeper than tureens. And the god-almighty devil and the fool That meet me in the High Street on the strike, When I walk about my heart a-gathering wool, Are my good and evil angels if you like. And both of them together in every kind of weather Ride me like a double-seated bike.
T.S. Eliot is not a single figure but a household. This household has, I think, at least three permanent residents. First, there is the archdeacon, who believes in and practices order, discipline, and good manners, social and intellectual, with a thoroughly Anglican distaste for evangelical excess.... And, no wonder, for the poor gentleman is condemned to be domiciled with a figure of a very different stamp, a violent and passionate old peasant grandmother, who has witnessed murder, rape, pogroms, famine, flood, fire, everything; who has looked into the abyss and, unless restrained, would scream the house down.... Last, as if this state of affairs were not difficult enough, there is a young boy who likes to play slightly malicious jokes. The too earnest guest, who has come to interview the Reverend, is startled and bewildered in being handed an explosive cigar.
One possible diagnosis of what went wrong with Victorian poetry -- and more generally with Victorian writing -- is that the diction got stratified to such a degree that you couldn't sensibly talk about seas in the same register as tureens; the only ways around this were to write in dialect or at least in brogue, or to use images that were in some sense explicitly comic. Davidson's poem, in the parts that work, does a bit of both but I think depends chiefly on deniability-through-comedy; his use of the outlandish but up-to-date image is very like what Eliot does in the first few paragraphs of "Prufrock."