From the second edition (1989):
Tom and Jerry
Names of the two chief characters in Egan's Life in London, 1821, and its continuation, 1828; whence in various allusive and attributive uses, esp. as name of a compound alcoholic drink, a kind of highly-spiced punch (U.S.); and attrib. in Tom and Jerry shop (Engl.), a low beer-house. Hence Tom-and-Jerry v., intr. to drink and indulge in riotous behaviour, like young bloods of the Regency period; Tom-and-Jerryism, drunken roistering, window-breaking, and the like.
The title of Egan's original work (1821) is ‘Life in London, or Days and Nights of Jerry Hawthorne and his elegant friend Corinthian Tom’; that of the continuation of 1828 is ‘Finish to the Adventures of Tom, Jerry, and Logic’, whence app. the order of the names in Tom and Jerry.

(Tom and Jerry shop was app. an expansion of the earlier Jerry-shop ‘a low beer-house’ (in Preston Temperance Advocate Mar. 1834, 18/2), which had no original connexion with Tom and Jerry.)

1828 Lights & Shades I. 124 No drinking and raking. No Tom-and-Jerrying in those days. 1829 W. Irving in Life & Lett. (1864) II. 387 We are too apt to take our ideas of English life from such vulgar sources as Tom and Jerry, and we appear to be Tom and Jerrying it to perfection in New York. 1852 Mundy Our Antipodes (1857) 207 As the glazier prays for hail-storms, civic riots, and the revival of Tom-and-Jerryism, for his own private ends! 1862 Jerry Thomas How to mix Drinks (N.Y.) 69 [Recipe]. Ibid., To deal out Tom and Jerry to Customers. Ibid., Adepts at the bar in serving Tom and Jerry [etc.]. 1865 Slang Dict., Tom and Jerry [ed. 1873 adds shop], a low drinking shop. 1880 Barman's Man. 47 [Recipe for Tom and Jerry]. 1884 S. Dowell Taxation II. 277 Free trade in beer in over 31,000 ‘Tom and Jerry’ shops, as the new beer-houses and shops were termed. 1894 Northumbld. Gloss., Tom-and-Jerry, a catcall. 1899 Morrow Bohem. Paris 305 Sipping Manhattan cocktails with a cherry-brandy-and-soda, Tom-and-Jerry, and the rest. 1903 Farmer & Henley Slang Dict., Tom-and-Jerry days, the period of the Regency (1810–20); also, ‘when George IV was king’.