The earliest Google Books pipe dreams
As Josh notes in his question, the earliest match for "pipe-dreams" in a Google Books search is from Grantley Berkeley, "The Fair Doe of Fernditch," in Tales of Life and Death, volume 1 (1870):
Among an infinity of sniffs, shrugs of shoulders, very audible sighs amounting to stifled groans, and tossings of the head, Mrs. Mantisser proceeded to render up the accounts, the housemaid who for the present to succeed her, having been ordered by Mr. Hastings, in a very feverish and peculiar manner, never to leave the room during the course of these proceedings, as if he had some reason or other for dreading a tête-à-tête, lively in his remembrance—perhaps the unwelcome conclusion to his last night's pipe-dream. [page 71]
But as StoneyB observes in a comment beneath the question, the story is quite clear that the "pipe-dream" in question were occasioned by Mr. Hastings's having smoked tobacco in a pipe prior to falling asleep:
'Your bit of nonsense! Why, cogs wounds! what does the woman mean? Whose been putting upon you? There, leave me, and I'll look into it tomorrow." So saying, Mr. Hastings sank into his easy chair, and commenced to stuff the bowl of his pipe with tobacco. [page 64]
"Ah that beautiful Fair Doe," sighed the smoker.—Puff, puff.—"Damn her impudence, that old housekeeper of mine; she's turned forty, and ought to know better. I keep a servant, not a mistress; leastways, so I will it, and she shall go! It don't do to let that class get the upper hand."—Puff, puff.—"I'll pension her off. She may go and prey on the human flock, not on me, and find if she can, a sky pilot, to fasten her talons on some fool forever."—Puff, puff, puff.—As he finished this sentence and with the last whiff of his pipe, very unlike his usual wont, which was to repair instantly to bed, he fell into a deep sleep,—deep all save his legs, which kept kicking about with the fidgets,—and shortly after he began to dream. [pages 65–66]
But the next-earliest Google Books match for "pipe-dream" is from a book published 21 years later in Chicago, Illinois—and the pipe involved in that pipe-dream is a Pan pipe. From James Blake, "Syrinx," in St. Solifer with Other Worthies and Unworthies (1891):
Pan dreamed of the pipe. The dream haunted him continually, and was to his spirit as the air he breathed was to his body. He had a dream of a wonderful music and voice which was to be made by a pipe, if only he could discover the pipe, or the wood of which it must be made, or the right shape and making of it.
So Syrinx, filled with the pipe-dream and the music, staid with Pan, looking about daily with as faithful eyes as his own. And the dream, and the search, and the wandering, which had been a sadness, now became a joy to Pan; for one pure sympathy and one brave heart, sharing his dream and believing in it, and rejoicing to see him in the light of it, was a wold of strength.
And the next Google Books match after that is from 1895, after the "opium pipe" sense of "pipe dream" was already established.
Early newspaper pipe dreams
Elephind and Library of Congress searches for "pipe dream" and "pipedream" yield a flurry of matches from late 1894 and throughout 1895.
The earliest match is from "Early Throes of Reform: The Seventy in a State Resembling Acute Colic," in the [New York] Sun (November 25, 1894):
"What are the nature of the charges against John C. Sheehan?"
"Well, I won't tell that, but they have to do with his proceedings on election day. The charges are strong and we can convict him, but heaven and earth will be moved to defeat us."
In the Second district around Chinatown they have a name for stories like this. They call them "pipe dreams."
These pipe dreams were not told to THE SUN reporter alone. They were circulated freely among the [Committee of] Seventy and the reformers.
The mention here of Chinatown (in lower Manhattan) is undoubtedly a reference to opium smoking, popularly associated with Chinese immigrants in New York, San Francisco, and elsewhere in the United States in the late nineteenth century.
The next match is again from the Sun, two days later, in "Col. Fellows Off to Albany" (November 27, 1894):
The reformers talked yesterday about a story that Col. Fellows would resign his office. If such a thing is possible this story is more foolish than the other pipe dreams. There is not a remote possibility of such a thing.
And the third is from the Sun in early 1895. From "Chimmie Fadden's Music Gale" (January 13, 1895):
"I was peepin' tru de curtain and I seed Miss Fannie and his Whiskers and Mr. Burton look at each odder like dey didn't know what t'ell; but Mr. Paul he looked up solemn as if dere wasn't a nodder small bet on eart'.
"Den de curtain was histed and I goes out feelin' like I was in a pipe dream and I sings de song.
Although the speaker here, Jimmy Fadden, has an Irish accent, he identifies himself as a "Bowery boy," which places him in New York City a few blocks away from Chinatown.
An interesting allusion the term occurs in an article originally published in the Chicago Tribune, and reprinted in the Rock Island [Illinois] Argus as "Fatality of a Name: A Strange Incident Which Suggests Mental Telepathy" (September 7, 1895):
Writers of fiction have no monopoly of the strange or supernatural. There are things taking place every day in Chicago which are as devoid of rational explanation as the mysterious coinings of the novelist's brain. Newspaper men hear of them, but in the rush for cold, hard facts, demanded both by city editors and newspaper readers, the "pipe stories," as queer and unexplainable happenings are called in journalistic circles, are at a discount. Were it not for this the following incident, which can be verified by the word of several reputable men, would long ago have received the space and attention it merits instead of being consigned to the wastebasket as the "pipe dream" of an opium devotee:
Early newspaper pipe stories
Matches for the term "pipe story" (in the sense of "fantastical story") go back somewhat farther than matches for "pipe dream"—but it isn't altogether clear whether the figurative pipe alluded to in the term was in those early days imagined to be filled with opium. From "Young but Tough: A Four-Year-Old Incorrigible Sent to the Reform School," in the St. Paul [Minnesota] Daily Globe (June 7, 1889):
The urchin will not live at home, and during the past year has been repeatedly picked up on the streets at night and kindly taken to some one of the stations for shelter. Then he would give a fictitious name, sometimes one and sometimes another, and tell a pitiful story of woe that not infrequently brought tears top the eyes of the good-natured coppers, who gathered around him. Sometimes he had been driven from home by heartless parents because he could not bring home pennies enough when sent out upon the street to beg. Another time his parents had died and left him without a relative or friend in the world, and he had wandered about the city for days, with only dry goods boxes to shelter him, and such food as he could pick up. And again he had been brought to the city and deserted by his parents at the union depot. ... But in the morning, or before, some one always put in an appearance at the station in search of him and the little romancer would be hustled away in disgrace. The police, however, finally got "onto" his pipe stories, in one station after another, and he was yesterday arrested and taken before the court. After hearing the case, Judge Burr decided that reform school was the best place for him, and referred him to the district court, with a recommendation to that effect.
And from the New York Sun (again) in a story titled "Big Faro Winnings: Stories of Heavy Playing by Enterprising Western Gamblers" (July 28, 1889):
"A hundred to one, bookmakers' odds, he didn't make that [$75,000] winnin'," said "One-armed" Schimmel.
John gave vent to this remark on reading what he called the pipe story. A small but select circle of experts in the green baize business sat around a table in the rear room of a Clark street saloon discussing Mr. Reschler's alleged phenomenal winning.
The expression became fairly widespread in the early 1890s, most notably in "Told a Pipe Story: Gordon Has Queer Fancies of a Conspiracy Against Him," in the St. Paul Daily Globe (again) (June 27, 1892):
The half crazed individual who said his name was George Gordon, arrested yesterday morning, is now in the county jail. Gordon, the city physician says, is either cray or under the influence of some narcotic. He related to the police yesterday a pipe story, about being pursued by a man who was endeavoring to poison him.
Also, from "Deluded to the Last: An Imaginative Gentleman Reads Bulletins to the Republicans," in the [New York] Sun (again) (November 9, 1892):
This man [reading telegrams to an assembled crowd at the Republican National Headquarters on election night] knew what he was laughing at. He confidentially called them "pipe stories." When he announced at 10 o'clock "Indian gives Harrison 30,000 plurality," the crown yelled itself hoarse.
The announcer got off his perch for a glass of water, and remarked to THE SUN reporter, "Gee, but that was a pipe story. I meant Pennsylvania." This man's mistakes were not responsible for all the "pipe stories." Most of them came down from the National Committee's room up stairs in the shape of bulletins.
And from the Omaha [Nebraska] Daily Bee (August 6, 1893):
A pipe story comes from Louisville that Bill Barnie has started south with $10,000 in "ready cash" to buy up good talent.
The Elephind and Library of Congress searches I ran did not turn up the 1890 instance cited by OED from the Chicago [Illinois] Daily Tribune. Instead, they yielded matches in which New York City was the earliest locale where "pipe dream" was in use as a slang term meaning fantasy—dating to 1894.
However, a possibly related term, "pipe story," was in use before 1894 in New York City; St. Paul, Minnesota; and Omaha, Nebraska. The earliest of these matches is from 1889 in St Paul. I couldn't find any decisive evidence that "pipe story" in its earliest occurrences alluded to an opium pipe (as opposed to a plain tobacco pipe, such as one might smoke while sitting with others and swapping tales), although the June 27, 1892, St. Paul Daily Globe story does tie the term to a person whom it describes as either insane or drugged.
For its part, "pipe dream" is associated with opium smoking from the outset of the newspaper matches I found (November 25, 1894). From the evidence I have on hand, it seems likely that both expressions are of U.S. origin and possible (but by no means certain) that "pipe story" influenced the emergence of "pipe dream," since the two terms have similar meanings.
As for the 1870 instance of "pipe-dream" from Great Britain involving a tobacco pipe smoker, I see no evidence that this occurrence of the wording was anything but coincidental. Database searches do not yield any additional instances of the term over the next twenty years anywhere—and when matches do begin to appear in the 1890s, they do so first in the United States and only later (and rarely) in the 1890s in the UK.
A search of the British Newspaper Archive yields one match from the London Morning Post (October 24, 1861) involving something that (I gather) is described as being "like an opium-pipe dream"—but that instance seemingly involves a simile rather than an idiomatic term. (I don't have a subscription to this website and so cannot confirm the wording or elaborate on the context of the rather garbled language that appears on the search page that I linked to earlier.)
The next-earliest matches for "pipe dream" from the same British database are from 1896 and 1899. Of these, the most interesting is this one, from the Dublin Daily Nation (September 28, 1899):
Nationalists have been thinking that yourself and your co-secretaries have been rather indulging in what our Yankee friends call "pipe dreams," over the matter.
It thus appears that, in the late 1800s, at least one Irish reporter or parliamentarian (the context of the extract suggests the latter) considered "pipe dream" to be a U.S. English idiom.