Green’s Dictionary of Slang

toby-lifting n.

[? ext. use of toby n.1 (1) on model of keister n.]

(UK Und.) luggage stealing at railway stations; thus toby-lifter n.

[UK]O.C. Malvery Soul Market 290: The men who came were adept at luggage stealing at the London termini. This system of crime [...] is known as ‘toby-lifting’ by the rogues who practice it.
[UK]E. Raymond Marsh 124: Robbers were [...] draggers, toby-lifters and sneak-thieves.