E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Like old boots. Famously, Cheeky as old boots, very saucy. He ran like old boots, i.e. very fast. The reference is to the nursery story of the Seven-leagued Boots, old being simply a word of fondness, as Well, old boy, etc. The allusion, suitable enough in many phrases, becomes, when used in slang, very remotely applicable.