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In reference to the remote South-Atlantic island of St. Helena, the nautical phrase to roll down to St. Helena, and its variants, mean, of a vessel: to advance steadily under a favourable wind, without having to change tack or sail.

Here, the verb roll means, of a vessel: to move along with a swaying motion.

The following definition of the phrase to roll down to St. Helena, for example, is from The Sailor’s Word-Book: An Alphabetical Digest of Nautical Terms (London: Blackie and Son, 1867), by the Royal-Navy officer William Henry Smyth (1788-1865) [page 578]:

ROLLING DOWN TO ST. HELENA. Running with a flowing sheet by the trade-wind.

Gershom Bradford (1879-1978), nautical engineer for the Hydrographic Office, United States Navy, explained the origin of the phrase to roll down to St. Helena as follows in A Glossary of Sea Terms (New York: Yachting, Inc., 1927) [page 144, column 1]—the Cape of Good Hope is a headland on the Atlantic coast of the Cape Peninsula in South Africa—the noun stunsail designates an additional sail set at the end of a yard to increase the ship’s speed in a fair wind:

ROLLING DOWN TO ST. HELENA, a romantic phrase used on the old sailing route from the Far East. It applied to that part of the voyage within the southeast trades on the run from the Cape of Good Hope to St. Helena. The weather is exceptionally fine with a long even swell, and the steady winds allowed the use of stun’sails alow and aloft.

These are, in chronological order, the earliest occurrences of the phrase to roll down to St. Helena and variants that I have found:

1-: From A Narrative of the Expedition to, and the Storming of Buenos Ayres, by the British Army, commanded by Lieutenant-General Whitelocke. By an Officer, attached to the Expedition (Bath: Printed by William Meyler, 1807) [page 4]—the noun pampero, also pamperos, designates a wind blowing from the Andes across the pampas to the Atlantic, accompanied by rain and thunder:

We reached the Cape and anchored in False Bay on the 19^th of March, from whence (on discovering that a place, where neither bread nor water could be procured, was not immediately adapted for refitting an Expedition) we proceeded to the town itself. We remained there a fortnight, during which period dispatches arrived from England which changed our destination; leaving no doubt remaining that we should follow a vessel with powder to South America; but lest we should arrive before the Panperos [sic], which are heavy gales of wind blowing down the river, we rolled down to St. Helena, where we amused ourselves about a week with Courts of Inquiry, Courts Martial, Cashiering, &c. at last “nous voila parti.”

2-: From The Pressed Man. A Tale of the Coast, published in The Drogheda Journal; Or, Meath and Louth Advertiser (Drogheda, Louth, Ireland) of Saturday 22^nd May 1830 [page 4, column 4]:

The corvette rounded the Cape, after hammering for a week against a nor-wester; rolled down to St. Helena, and was already making Teneriffe’s lofty peak, when, for the first time during her long voyage, a sail decidedly inimical claimed her attention.

3-: From The Angler in Wales, or, Days and Nights of Sportsmen (London: Richard Bentley, 1834), by the British author Thomas Medwin (1788-1869) [volume 2, Eighteenth Day. (Continued.), page 19]:

“You have heard of rolling down from the Cape to St. Helena; almost at all seasons of the year, it blows from the same quarter very nearly a gale of wind, by which Napoléon’s delightful abode was swept, whilst the government-house, which ought to have been given up to him, has the advantage of being completely abrité.”

4-: From The Western Messenger; Devoted to Religion and Literature (Cincinnati (Ohio): Printed by James B. Marshall) of July 1836 [page 831]:

ART. 8.—HOMEWARD BOUND.
Written off St. Helena, Aug. 6, 1835; Lat. 25 deg. 29 min. Long. 3 deg. 19 min.

Rolling down to St. Helena, homeward bound we go,
Right before the south-east trades that fresh and strongly blow,
With studding sails ’low and aloft, all full and drawing well,
Merrily we roll along before the heaving swell.
[…]
Eight knots we’re running by the log, all foaming is the sea,
And rolling down to St. Helena, homeward bound are we!