No one gives you a thought, as day by day
You drag your feet, clay-thick with misery.
None think how stalemate in you grinds away,
Holding your spinning wheels an inch too high
To bite on earth. The mind, it's said, is free:
But not your minds. They, rusted stiff, admit
Only what will accuse or horrify,
Like slot-machines only bent pennies fit.
So year by year your tense unfinished faces
Sink further from the light. No one pretends
To want to help you now. For interest passes
Always towards the young and more insistent,
And skirts locked rooms where a hired darkness ends
Your long defence against the non-existent.
In some ways this seems a harsh, unlovely, and ungenerous piece, but on the other hand it has its accuracies. When it was written, in 1949 according to my volume, "neurosis" of course was a commonplace term owing to the cultural prominence of psychoanalysis. Neurosis remains a widely recognizable term, of course, but one no longer finds it in mainstream psychiatric diagnosis, as it has been split into myriad anxiety, mood, and perhaps personality disorders.
However, the construct of "neuroticism," which is a general tendency to emotional negativity and instability and susceptibility to stress, still exists as one of five major components of personality as identified in psychological testing (the other four are openness vs. conventionality, conscientiousness vs. expediency, extroversion vs. introversion, and agreeability vs. its lack). Neuroticism is correlated with increased risk for depression, anxiety, and eating disorders among other things. To my mind, describing someone as broadly neurotic can be more helpful and convenient than listing the five DSM-IV diagnoses they may happen to meet criteria for.
As for Larkin's poem, it painfully depicts the disfiguring and ostracizing effects that neuroticism can have; no, it is not (quite) leprosy, but it can alienate almost as much. It conveys the sense of stasis and sluggishness ("clay-thick"), of emotional torpor that results not from repose, but from wasteful psychological exertion (the metaphor of wheels spinning but gaining no traction on earth is just right).
Larkin puts his finger on the core problem of neurosis, which is the lack of internal freedom; while philosophers forever debate freedom vs. determinism in the abstract, the neurotic battles fatalism on a daily basis. Cheer up; don't be afraid; eat less; exercise. How can these things seem so impossible? For one thing, the neurotic lives in a different perceptual world from the rest of us, with a mind that will "admit only what will accuse or horrify."
"Tense unfinished faces" is perfect, suggesting the way in which anxiety inhibits and blurs individuation. There is a sense in which neurosis is a disabled identity. I'm not sure that "hired darkness" works as well, but I assume Larkin means here the classic avoidance by which the neurotic seeks to fend off "non-existent" threats, although ironically the threats in question are in reality all-too-existent, merely within the neurotic's "locked rooms," and not without as he imagines.