Mid 19th century; earliest use found in The Pall Mall Gazette. Probably from naggle (although this is first attested slightly later). Compare slightly later naggling.
naggle2
/ˈnaɡl/
ChieflyBritish regional
verb
[no object]To gnaw, bite.
Origin
Mid 19th century; earliest use found in John C. Atkinson (1814–1900), author and antiquary. From nag + -le.