[Self-answering after doing some digging.]
It's a criticism of Tolstoy's Christian beliefs, which he commited to in a late stage of his life, after experiencing an existential crisis, detailed in his book Confession (published in 1882).
In 1890, Tolstoy's The Kreutzer Sonata was published (see its publication history). As described in Wikipedia:
The work is an argument for the ideal of sexual abstinence and an in-depth first-person description of jealous rage. The main character, Pozdnyshev, relates the events leading up to his killing of his wife: in his analysis, the root causes for the deed were the "animal excesses" and "swinish connection" governing the relation between the sexes.
On that same year, Tolstoy published an "epilogue" explaining his novel, following requests from readers. An excerpt (source):
[F]alling in love and connection [...] never facilitate, but always impede, the attainment of any aim worthy of man.
- The epilogue cited in Wikipedia cites the same sentence (it's the last one over there), but uses a different translation (this one).
In 1963, after reading Tolstoy's novel, Hughes had written a poem of the same name. This is its final stanza:
Rest in peace, Tolstoy!
It must have taken supernatural greed
To need to corner all the meat in the world,
Even from your own hunger.
In Ted Hughes As A Shepherd Of Being, the author sees it as an attack on Tolstoy's puritanism (source):
In Kreuzer Sonata, the you addressed is both Tolstoy and Pozdnushev, his puppet. It is [...] an attack upon Tolstoy's ultra-puritanism and its consequences.
No evidence is brought forward in Tolstoy's story that adultery has been committed. For neither Pozdnyshev nor his author does this matter. The murder is justified [...] on moral grounds.
[T]he murder is also self-murder [...] since her death marks a final intensification and crystallisation of the death-in-life which his extreme puritanism imposes on him. After his acquittal, Pozdnyshev refuses to have anything whatever to do with sex. He is in fact dead, and Hughes in the final stanza transfers this death to Tolstoy himself.
That same criticism is expressed in Revenge Fable, attacking Tolstoy for holding values that forbids and condemns love, and by extension - life itself, whose vital forces are described as the Mother in this poem (and others).
What got me off to begin with was that Tolstoy held an anarcho-Christian beliefs and opposed the church (which led to his excommunication in 1901) - so I figured, by mistake, that Hughes and him were "on the same side" against the institutional Christianity.
An early assault on Tolstoy's ideas was expressed by DH Lawrence (see in length in D. H. Lawrence's response to Russian literature), in his "Study of Thomas Hardy" (published in 1914, partial text here), and later in his 1925 essay "The Novel" (published in 1968 in Phoenix II, which is later to Hughes' Kreuzer Sonata).
- It should be noted that DH Lawrence attacks Tolstoy's writing as a whole, and is not concerend with the three stages he went through (pre-conversion, conversion, post-conversion).
The following excerpt is from "The Novel" essay:
[...] Tolstoi, in his metaphysic, renounced the flesh altogether [...] But above all things, Tolstoi was a child of the Law, he belonged to the Father. He had a marvellous sensuous understanding, and very little clarity of mind.