(bl&g) [Etym. unknown.]
Robbery (with violence); theft.
1885 Session Paper 30 July 471 There has been another blag down round here. 1936 J. Curtis Gilt Kid 22, I don't want to say ‘O.K.’ and then find out that I've let myself in for+doing a blag on the crown jewels. 1960 Observer 24 Jan. 5/1 The top screwing teams, the ones who went in for the really big blags, violent robberies.

Hence blag v., to rob (with violence); to steal. So "blagger, one who blags.
1933 C. E. Leach On Top of Underworld x. 137 Blag, snatch a watch chain right off. 1938 F. D. Sharpe S. of Flying Squad i. 15 Blaggers, screwsmen, [etc.]+abound in the Underworld of London. Ibid. 329 ‘Johnny blagged the till’—Johnny took the till. 1945 J. Henry What Price Crime? 93 Another is known as the ‘blagger’ or ‘snatcher’. These are usually young louts who specialize in snatching ladies' handbags and bolting off.


perhaps it's a blend of bag and lag; take a look at these citations:
(l&g)
†1. trans. To carry off, steal. Obs.
1573 Tusser Husb. xx. (1878) 54 Some corne away lag in bottle and bag. Some steales, for a iest, egges out of the nest. Ibid. xxxvi. 86 Poore cunnie, so bagged, is soone ouer lagged.

(b&g) trans.
6. colloq. a. To seize, catch, take possession of, steal. To add to one's ‘bag’ (bag n. 9). fig.