Green’s Dictionary of Slang

1. (also strap to) to work hard, to get on with, to buckle down to [one applies the fig. strap to one’s own back].

1811		Lex. Balatronicum n.p.: to strap. To work. The kiddy would not strap, so he went on the scamp: the lad would not work, and therefore robbed on the highway.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue [as cit. 1811].
1937–84		Partridge DSUE (1984) 1164: strap v.i. to work [...] Also with away (1849) and to [...] from ca. 1810; ob. by 1930.

2. to interrogate [one applies the fig. strap to another’s back].

1989

J. Morton Lowspeak 134: To interrogate harshly.