WordNet
up to his neck
adj. deeply involved; "neck-deep in work"; "up to their necks in debt" [syn: neck-deep, up to my neck, up to your neck, up to her neck, up to our necks, up to their necks]
Wikipedia
Up to His Neck
Up to His Neck is a 1954 British comedy film directed by John Paddy Carstairs and starring Ronald Shiner as Jack Carter, Hattie Jacques as Rakiki and Anthony Newley as Tommy.