Two cites for this word in OED, one from Tolkien, assert that it derives from T.W. Earp, a student at Oxford who matriculated in 1911. (The earliest cite is from a book called Soldier & Sailor Words, 1925.
1944 J. R. R. Tolkien Let. 6 Oct. (1981) 94 He lived in O[xford] at the time when we lived in Pusey Street (rooming with Walton, the composer, and going about with T. W. Earp, the original twerp).
1957 R. Campbell Portugal 87 T. W. Earp (who gave the English language the word twirp, really twearp, because of the Goering-like wrath he kindled in the hearts of the rugger-playing stalwarts at Oxford, when he was president of the Union, by being the last, most charming, and wittiest of the ‘decadents’).
OED remains unconvinced, stating ‘of uncertain origin’ although it does mention the T.W. Earp possibility. I wonder if any evidence for or against the Earp origin has turned up since the 1986 entry. I also wondered whether the term is used in the US but the cites from John O’Hara, Ezra Pound and Sinclair Lewis seem to answer that satisfactorily.