WITTY, lively, satirical, moral — at Tate Britain, such words will be heard often over the coming months, since the gallery’s exhibition of the works of William Hogarth has just opened there, after a spell in Paris, and before it goes to Barcelona.

This is a splendid opportunity to see the artist’s “comic histories”, his magnificent paintings and prints, side by side: A Rake’s Progress in the same room as A Harlot’s Progress, Marriage A-La-Mode not far from The Four Times of Day — and set in a copious context of drawings, engravings, books, newspapers, sculpture, even woodcuts. But there is another quality to Hogarth’s wonderfully vivid visions of 18th-century England, a quality with which the artist is perhaps not much associated: piety.

Amid the tumble of the street scenes, for example, one of the most striking of the paintings on display at the Tate is also one of the most plainly pious. In the corner of a room devoted to “The English Face”, next to the controversial Bishop of Winchester, Benjamin Hoadly, sits Thomas Herring, Archbishop of Canterbury. Whereas Hoadly is dressed almost gaudily, bedecked to suit his role as Prelate of the Order of the Garter, a stained-glass window colourfully upstaging him, Herring is dressed simply and framed without distractions. He could be practically any Anglican clergyman, let alone a bishop. In one hand, he holds a book (guess which one), and with the other he gestures, as if caught mid-conversation with the artist. His face is open and lively, and his eye is bright; the next sentence is forming on his lips.

It is a likeable image, but Hogarth was criticised for painting it — for eschewing the placidity that was the custom in such ecclesiastical commissions. (Herring, incidentally, went through a see change during the period of the portrait’s production, moving from York to Canterbury in the mid-1740s.) The artist, however, could not have paid Herring a finer compliment.

Compare this portrait with two portraits of laymen more prominently displayed in the same room: George Arnold, a successful merchant, and Thomas Coram, whose portrait Hogarth painted for the Foundling Hospital, the institution that Coram had established. Like the portrait of the Archbishop, these are uncluttered images, dignified, unfussy, squarely concentrating on the sitter. These are men, the painter would seem to say, who deserve your respectful and undivided attention.

It is a pity, then, that they could not have been joined at the Tate by Hogarth’s portrait of the equally admirable Daniel Lock, the architect who built the Foundling Hospital. Absent, too, are the large, now fragile canvases The Pool of Bethesda and The Good Samaritan, which he painted in 1735-36 for St Bartholomew’s Hospital, where they still reside. But there are other things here that suggest the extent to which Christianity shaped Hogarth’s vision of the world around him. Another work that he donated to the Foundling Hospital is his ambitious painting of the child Moses in Egypt, looking vulnerable and tentative, surrounded by exotic oddities.

There are the biblical inscriptions that accompany the various stages of Industry and Idleness (1747). And there is the daring depiction of the notorious Sir Francis Dashwood “at his devotions”, a libertine saint kneeling in adoration before his deity — a voluptuous, reclining nude. Dashwood’s halo incorporates the profile of an associate, whispering temptation in his ear.

Among the first and last things also on display are some errant clergymen. In The Christening (1729), an early work, the priest is distracted from the baby in his arms by the sight of a female bosom on ample display beside him. Likewise, in the first scene of A Harlot’s Progress (1731), a clergyman on horseback is present when the young woman of the title arrives in London. But how can he possibly help her, as she is coaxed in the direction of a lecherous-looking old gentleman, when he hasn’t even noticed that his mount is knocking over a pile of plates?

Finally, on the last wall of the exhibition is the magnificent Election series (1754), in which, at a feast laid on for the voters by one of the competing political parties, a fat cleric mops his sweaty head with a handkerchief, his gluttonous eyes bulging as he prepares to tuck into the steaming dish before him.

When it comes to Hogarth, the devil is always in such details. We know how bad things are between the unhappy couple in Marriage A-La-Mode (1743) by what is carefully scattered around them. But God is there, too, in the minutiae. So overpowering is the figure of David Garrick in the famous painting of the actor as Richard III waking from his bad dreams before the Battle of Bosworth, that the casual viewer might easily miss the (actually quite large) object behind the King in his tent: a wooden carving of Christ on the cross. The import of the scene is clear. Like many a sinner in Hogarth’s more riotous scenes, Richard has turned his back on Christ.

We might see lots of things at the Tate, including beautiful brushwork and the tender use of colour, or a sense of humour and a social conscience. Hogarth wants us to see these things. But there are more things . . . and he wants us to see them, too.

The exhibition “Hogarth” runs at the Linbury Galleries, Tate Britain, Millbank, London SW1, until 29 April. Phone 020 7887 8888. www.tate.org.uk