According to Zythophile, the generally accepted story, though seemingly unsupported by evidence, is that after the Trademark Registration Act 1875 came into force, a Bass employee queued overnight outside the registrar’s office so the company would be first to file when registration opened on January 1st, 1876. This is why, in 2013, Bass Pale Ale was renamed Bass Trademark No.1.

The Guinness harp is another well known trademark registered in 1876. Registration date, of course, isn’t necessarily when a design was first used.
A list of the ten oldest company logos includes Shell, Stella Artois, Levi Strauss, Heinz, Peugeot, and Prudential, though I can’t vouch for the dates given. Via Brand New.

In a recent conversation about why logos endure, Michael Bierut said he believes the Bass triangle is the earliest known logo.
Comments
I guess we’d have to say that there’s a big difference between a trademark and a registered trademark, and the former is very much older than the latter.
There is evidence of fixed typographical cyphers used by traders as identifiers in Ancient Greece. Logos are really a part of all human cultures of power, whether we’re talking about businesses or the symbols of royal houses. By the Middle Ages, the company logo was exactly what it is today: not only logos for businesses, but also individual logos for the products produced by a business, designed to be suggestive of esoteric qualities appealing to particular customers.
The Bass logo is the oldest trademark, but only in Great Britain. Previously, the Czech trademark PILSNER (1859) and American trademark (1870) were registered. I wrote an extensive article on the topic: The oldest registered trademarks in the world.
The brewers of ancient Pompeii were trying to come up with a trade mark, when one of them, looking out of the window, said “how about that big volcan….Aaaaagh!” The name never caught on.