Green’s Dictionary of Slang

(UK Und.) to pickpocket at a racecourse; see 1938 cit.

1938		F.D. Sharpe Sharpe of the Flying Squad 201: Gangs of pickpockets would surround punters placing bets. The bookmaker, who could recognize all of them as notorious characters, was expected to loiter about his work in order to give them an opportunity to pick his clients’ pockets. This is called ‘Dwelling the box’.
1959		‘The Pickpocket’ in Encounter n.d. in Norman Norman’s London (1969) 66: The fourpenny snore and the sweeny / Dwell in the box for you. / So nitto, nark it, stoppo, / Or a carpet’s a lay-down for you.