In the course of putting together a book based on this blog (you heard it here first!), I found that I am standing on the shoulders of Richard Grant White. White, a nineteenth-century American literary critic (and father of the architect Stanford White), coined the word “Briticism” in 1868, to mean words and usages that had sprung up in Britain (but not America) in the century or so since the countries had been apart. White didn’t look kindly on this phenomenon. Among the instances he cited was a peculiar British use of the word “directly”:
Directly.—The radical meaning of this word is, in a right line, and hence, as a right line is the shortest distance between two points, it means at once, immediately. Its synonyme in both senses is a good English word, now, unhappily, somewhat obsolete, straightway—our equivalent of which, right away, is laughed at by brother Bull as an Americanism. But John Bull himself uses directly in a way which is quite insufferable—to wit, in the sense of when, as soon as. This use of the word is a widespread Briticism, and prevails even among the most cultivated writers. For instance, in the London “Spectator” of May 2, 1867, it is said that “Directly Mr. Disraeli finished speaking, Mr. Lowe rose to oppose,” etc. Anglice, As soon as Mr. Disraeli finished speaking, etc. It is difficult to trace by continuous steps the course of this strange perversion, for which there is neither justification nor palliation.
He also complained about a supposed British insistence on saying “ill” instead of “sick” to describe someone who was under the weather.
They sneer at us for not joining in the robbery and the imposition. I was present once when a British merchant receiving in his own house a Yankee youth at a little party, said, “Good evening! We haven’t seen you for a long while. Have you been seeck” (the sneer prolonged the word), “as you say in your country?” “No, thank you,” said the other, frankly and promptly, “I’ve been hill, as they say in yours.”
He went on, “For the use of ill—an adverb—as an adjective, thus: an ill man, there is no defence and no excuse, except the contamination of bad example.” Like many language peevers through the ages, he was on shaky ground. In fact there was nothing new about adjectival “ill”: “By my troth I am exceeding ill” is a line from Much Ado About Nothing).
Another complaint was “awfully” to mean “very,” instead of its early meaning of “in a manner that inspires awe or terror.” White wrote, “The misuse is a Briticism; but it has been spreading rapidly here during the last few years.” And here he was on the mark. In fact, I put forth this intensifier “awfully” as the very first Not One-Off-Britishism.
The early citations in the OED (which labels it “colloquial”) are all British, starting with one from The Times in 1820: “Let any one..say whether the illustrious defendant [sic]..has not awfully strong grounds for protesting against the tribunal.” I happen to be reading Thackeray’s Vanity Fair—published in 1847-48 and set in the 1810s—and came upon a line where Becky Sharp thinks, “I suppose he will be awfully proud, and that I shall be treated most contemptuously.”
Ngram Viewer also confirms White’s impression.

It’s an interesting chart, showing significantly more frequent use in Britain in the second half of the nineteenth century (White’s era), and American topping Britain in about 1920.
Since then, the two countries’ use of the word have been awfully similar.