Green’s Dictionary of Slang

beggar my neighbour phr.

also next door neighbour
[rhy. sl. = on the labour]

visiting the labour exchange/unemployment office to draw unemployment benefit.

[UK]Thieves Slang ms list from District Police Training Centre, Ryton-on-Dunsmore, Warwicks 7: Next door neighbour: On the labour (drawing unemployment pay).
[UK]J. Franklyn Dict. of Rhy. Sl.
[UK]R. Puxley Cockney Rabbit.