I'd certainly never heard it, but.

[Short for Tod Sloan (occas. used in full), name of a U.S. jockey (1874–1933), used as rhyming slang for ‘own’ in the phr. on one's own.]
on one's tod: alone, on one's own. Cf. Pat Malone.
1934 P. Allingham Cheapjack vi. 56 ‘Are you on your tod?’ I gathered that she was asking me if I was on my own. 1956 L. Godfrey in Pick of Today's Short Stories 91, I was in a small ward, and one evening some clot turned on the bloomin' wireless, and then went out, leaving me on my tod. 1959 J. Wain Travelling Woman 7 Frequent visits to town on your Tod Sloan—no need to account for your doings. Leave her to keep the home fires burning. 1966 T. E. B. Clarke Wide Open Door xi. 156 I'm on me Tod 'cept for the baby. 1972 J. Brown Chancer v. 64 That left Sonny and me on our tod in the public. 1981 ‘G. Gaunt’ Incomer xiii. 71 Maybe they don't want your company.+ Never seen you on your tod before.

they don't deign to tell us how a U.S. jockey got into London rhyming slang.