The verse that Denise Levertov borrowed for her poem, Beginners, was from a work by A. C. Swinburne (1837-1909).
I'm going to be lazy and lift a paragraph from Wikipedia:
Proserpine (sometimes spelt Proserpine, Prosperine or Prosperina) is an ancient Roman goddess whose story is the basis of a myth of Springtime. Her Greek goddess' equivalent is Persephone. The probable origin of her name comes from the Latin, "proserpere" or "to emerge," in respect to the growing of grain. Proserpina was subsumed by the cult of Libera, an ancient fertility goddess, wife of Liber and is also considered a life–death–rebirth deity. She was the daughter of Ceres, goddess of agriculture and crops and Jupiter, the god of sky and thunder.
The Garden of Proserpine by Algernon Charles Swinburne
Here, where the world is quiet; Here, where all trouble seems Dead winds' and spent waves' riot In doubtful dreams of dreams; I watch the green field growing For reaping folk and sowing For harvest-time and mowing, A sleepy world of streams.
I am tired of tears and laughter, And men that laugh and weep; Of what may come hereafter For men that sow to reap: I am weary of days and hours, Blown buds of barren flowers, Desires and dreams and powers And everything but sleep.
Here life has death for neighbor, And far from eye or ear Wan waves and wet winds labor, Weak ships and spirits steer; They drive adrift, and whither They wot not who make thither; But no such winds blow hither, And no such things grow here.
No growth of moor or coppice, No heather-flower or vine, But bloomless buds of poppies, Green grapes of Proserpine, Pale beds of blowing rushes, Where no leaf blooms or blushes Save this whereout she crushes For dead men deadly wine.
Pale, without name or number, In fruitless fields of corn, They bow themselves and slumber All night till light is born; And like a soul belated, In hell and heaven unmated, By cloud and mist abated Comes out of darkness morn.
Though one were strong as seven, He too with death shall dwell, Nor wake with wings in heaven, Nor weep for pains in hell; Though one were fair as roses, His beauty clouds and closes; And well though love reposes, In the end it is not well.
Pale, beyond porch and portal, Crowned with calm leaves she stands Who gathers all things mortal With cold immortal hands; Her languid lips are sweeter Than love's who fears to greet her, To men that mix and meet her From many times and lands.
She waits for each and other, She waits for all men born; Forgets the earth her mother, The life of fruits and corn; And spring and seed and swallow Take wing for her and follow Where summer song rings hollow And flowers are put to scorn.
There go the loves that wither, The old loves with wearier wings; And all dead years draw thither, And all disastrous things; Dead dreams of days forsaken, Blind buds that snows have shaken, Wild leaves that winds have taken, Red strays of ruined springs.
We are not sure of sorrow; And joy was never sure; To-day will die to-morrow; Time stoops to no man's lure; And love, grown faint and fretful, With lips but half regretful Sighs, and with eyes forgetful Weeps that no loves endure.
From too much love of living, From hope and fear set free, We thank with brief thanksgiving Whatever gods may be That no life lives for ever; That dead men rise up never; That even the weariest river Winds somewhere safe to sea.
Then star nor sun shall waken, Nor any change of light: Nor sound of waters shaken, Nor any sound or sight: Nor wintry leaves nor vernal, Nor days nor things diurnal; Only the sleep eternal In an eternal night.
I agree that poetry is meant to be heard and not just read, so John Gielgud has graciously agreed to help with that:
And from the 11th Edition of Encyclopaedia Britannica (1911)
PROSERPINE (Proserpina), the Latin form of Persephone,' a Greek goddess, daughter of Zeus and the earth-goddess Demeter. In Greek mythology Demeter and Proserpine were closely associated, being known together as the two goddesses, the venerable or august goddesses, sometimes as the great goddesses. Proserpine herself was commonly known as the daughter (Core), sometimes as the first-born.
As she was gathering flowers with her playmates in a meadow, the earth opened and Pluto, god of the dead, appeared and carried her off to be his queen in the world below. This legend was localized in various places, as at Eleusis, Lerna, and "that fair field of Enna" in Sicily. Torch in hand, her sorrowing mother sought her through the wide world, and finding her not she forbade the earth to put forth its increase.
So all that year not a blade of corn grew on the earth, and men would have died of hunger if Zeus had not persuaded Pluto to let Proserpine go. But before he let her go Pluto made her eat the seed of a pomegranate, and thus she could not stay away from him for ever.
So it was arranged that she should spend two-thirds (according to later authors, one-half) of every year with her mother and the heavenly gods, and should pass the rest of the year with Pluto beneath the earth. There can be little doubt that this is a mythological expression for the growth of vegetation in spring and its disappearance in autumn. According to Theopompus there was a Western people who actually called the spring Proserpine.
As wife of Pluto, she sent spectres, ruled the ghosts, and carried into effect the curses of men. The lake of Avernus, as an entrance to the infernal regions, was sacred to her. From the head of a dying person Proserpine was supposed to cut a lock of hair which had been kept sacred and unshorn through life.
She was sometimes identified with Hecate. On the other hand in her character of goddess of the spring she was honoured with flower-festivals in Sicily and at Hipponium in Italy. Sicily was a favourite haunt of the two. Some, however, regard Proserpina as a native Latin form, not borrowed from the Greek, and connected with proserpere, meaning the goddess who aided the germination of the seed.