The modern use of the word arrived from the US during the 19th century.
It is quite a long way from the 14th-century usage, which came into the language from French, meaning a bag for carrying things on a journey, or knapsack.
Pilgrims and pedlars would carry wallets, and this type of use still has some currency today. It is how Ulysses uses the word, when he says to Achilles: "Time hath, my lord, a wallet at his backWherein he puts alms for oblivion" (Troilus and Cressida, III.iii.145).
Images of Time putting these alms into the equivalent of a modern wallet should be carefully avoided.
Shakespeare is the first recorded user of the word in an extended sense, meaning "protruding lump, bulging growth", when Gonzalo describes mountaineers "whose throats had hanging at 'em Wallets of flesh" (The Tempest, III.iii.47). The mountaineers are not folding their flesh and putting it into an inside jacket pocket.
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin