Green’s Dictionary of Slang

drum n.²

the road, the street.

a.1789		G. Parker (attrib.) ‘The Sandman’s Wedding’ in Farmer Musa Pedestris (1896) 64: Just as he turned the corner of the drum, His dear lov’d Bess, the bunter, chanc’d to come.
1856		H. Mayhew Great World of London I 6: Oh, I drop the main toper [...] and slink into the ken (lodging-house) in the back drum (street).
1858		A. Mayhew Paved with Gold 353: Instead of getting to some libb-ken, on the main toper, where a drop of lap could be had, you’re sticking to the back drums.
1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor I 217/2: We drop the main toper (go off the main road) and slink into the crib (house) in the back drum (street).
1877		J. Diprose London Life 80: [as cit 1856].
1906		A. McCormick Tinkler-Gypsies of Galloway 194: Road? ‘Drum,’ said William Marshall.

In phrases

on the drum

living as a tramp.

1835

Worcester Herald 26 Dec. 4/3: On the drum, one of the profession, or on the look out.