One of my characters uses the term 'old bill' when talking about the police. I did not think this should be 'Old Bill' but it has beed suggested to me it should.
I would capitalise it. Just did a quick search and both The Independent and The Official Encyclopedia of Scotland Yard capitalise it, so that's good enough for me.
Also, If a policeman is charging someone under the misuse of drugs act, should that have capitals? Misuse of Drugs Act.
According to my copy of Brewers it is capitalised because 'Old Bill' is a character and thus it's a proper noun. The suggestion they make is that Old Bill was originally a character created by Bruce Bairnsfather in the first world war; a cynical, long suffering, 'ours is not to reason why', nose to the boring grindstone old soldier. And apparently that character was used on recruitment posters for the Met after the war, and as a popular character being shown now in police uniform after the war the name transferred over. I do like this interpretation because it explains why it should be capitalized, which is a better reason that just because everyone else does. You could possibly argue that it's become a proper noun just by common usage but generic nouns are by definition not proper nouns. Which is probably why those people who use lower case use it for this. Because it's a generic noun, they don't know the allusion so they stick with what would otherwise make sense. Honestly; you can argue it either way but I would go with the popular spelling and capitalize. As an interesting addition; Bobbies should be capitalized because Bobby was Robert Peel (see also Peelers). But unlike the Old Bill which is a collective noun, a Bobby is one police officer, right? One Bobby but two Bobbies, right? But why? When pluralizing first names we don't drop the Y. So why are they bobbies on the beat? Because that's what everyone says, even though it should be a proper noun and it's a first name ending in Y. These slang words are in a really weird place, where they aren't quite proper nouns anymore and live in a weird grey area of writing.
Nobody is sure where the term came from - there are loads of theories - but most of them do trace back to an actual person called William/Bill, hence the capitalisation. There are theories that don't, like one that says the police used some kind of weapon called a bill. But it seems likely that Old Bill was always a proper noun.
The really interesting thing (that I edited in after you answered) is that Bobby is definitely drawn from a real person, from Robert Peel but isn't treated like a proper noun by seemingly anyone.
