A search on the phrase finds the author to be one RHD Barham. This is not the clergyman and author Richard Harris Barham, 1788–1845 (aka Thomas Ingoldsby, author of the classic Ingoldsby Legends) but his son, the Reverend Richard Harris Dalton Barham, who evidently inherited the talent for literate doggerel. As this article explains - The Ingoldsby Legends, Ingoldsby Country & Tappington Hall - the Barhams were a Kent family and RHD Barham the rector of Lolworth, Cambridgeshire - but the Devon connection is that RHD lived in Dawlish from 1863, and died there in 1886.
The "anchovy sauce" line comes from his poem The Monk of Haldon: A Legend of South Devon (see page 488, Temple Bar: A London Magazine, Volume 20, 1867), a picaresque yarn inspired by the remains of a chapel near Dawlish. It tells how the chapel and the associated holy well are tended by a succession of monks until a rough and sinister one, Friar John, takes over the post. A pirate, Sailor Jack, visits him one evening, and over a drinking session boasts about his loot. Friar John attempts to murder him, but Jack chokes him and throws him into the well. On later investigation, however, two corpses are found in the well, neither of them Friar John. The investigators find a cache of loot nearby, and cover up the well; Sailor Jack never encounters good fortune again. The reader is advised that the well is findable, but "to let well alone".
The relevant lines, a nice landscape description, are:
To the right, under Haldon,
Lie Teignmouth and Shaldon,
With hamlets, whose names to recount I'm not called on:
Between them the Teign rolls her eddying flood,
The stream looking tinted and turbid with blood;
But it's only the rain that has stirred up the mud!
It's certainly odd that this part of the coast,
While neighbouring Dorset gleams white as a ghost,
Should look like anchovy sauce spread upon toast!
We need not now pause
To find out the cause
Of this variation in natural laws;
But Mr. Pengelly
Can easily tell ye,—
(I think, by the way, that the gentleman said,
'Twas iron or manganese made it so red).
This geological flavour 1 is explicable by RHD Barham's interests:
Richard Harris Dalton Barham, son and biographer of the author of the "Ingoldsby Legends," was born at Westwell, Kent, in the month of October, 1815. He was educated at St. Paul's School and Oxford University, and followed his father, both in the choice of a profession, and as a contributor of mock-heroic stories in verse to Bentley's Magazine. Shortly after leaving Oxford he was presented with the living of Lolworth, near Cambridge, where he resided, until, in 1863, delicate health compelled him to seek a warmer climate, and he retired to Dawlish, where he pursued geological studies.
- page 365, The Poets and Poetry of the Nineteenth Century, Alfred H Miles, 1905 (Internet Archive poetspoetryofnin10mile)
His obituary in The Hampshire Advertiser on May 8th 1886 says that he spent days in searching the cliffs and quarries for fossil madrepores, a collection of which he presented to the town of Dawlish. Returning to the Miles book:
He published, besides the "Life and Letters" of his father (1870), "The Life and Remains" of Theodore Hook (1849), and a novel entitled "A Rubber of Life," [as Dalton Ingoldsby] which was afterwards dramatized for a London Theatre. "The Temptations of St. Anthony" ... is the best known and perhaps the best written of his verse tales, though, like some of his father's "Legends," it suffers from that facility of composition which so often proves fatal to felicity of style. In verse of this class it is so easy to be slovenly that one has frequently to regret spray-footed lines and hump-backed cadences, the more to be deplored that they are found in close proximity to stanzas wholly regular.
The Rev. R. H. Dalton Barham died at Dawlish on the 28th of April, 1886.
Addendum: I've followed the thread further at the Devon History Society weblog, concerning an episode in the last year of Barham's life, when he gave evidence in the investigation of a fatal accident at a Dawlish beach. See 1885: Dawlish "death trap".
Addendum 2: see also Angela Williams's Literary Places site, which has two posts about Barham: R. H. D. Barham at Dawlish tells of Angela's initally unsuccessful search for his grave at St Gregory's churchyard; and R. H. D. Barham’s grave visits its real location (the guidebook being wrong) in Dawlish cemetery.
1. Though admittedly with a geological error: the part of the coast that "gleams white as a ghost" visible from Dawlish is actually still in Devon. It's the Cretaceous chalk cliffs of Beer Head.