Entry from OED Online

[< OLD a. + Bill, pet-form of the male forename William (cf. BILLY n.²).
  The character of Old Bill was created by the British cartoonist Bruce Bairnsfather (1888-1959) and appeared in issues of Bystander from 1915 onwards.
  The origin of sense 2 is uncertain. It may have arisen from subsequent use of the cartoon character, depicted in police uniform, on posters in a Metropolitan Police recruitment campaign of 1917, and later during the Second World War (1939-45) giving advice on wartime security. Among other explanations that have been suggested are that it is from the association of police officers prior to the Second World War with ‘Old Bill’ moustaches; from the ‘bill’ (BILL n.¹ 2b, also BILLY n.² 1b) used as a weapon by 18th-cent. constables; or from the registration letters BYL originally used on cars belonging to the Flying Squad.] 

    1. a. The name of a cartoon character of the First World War (1914-18), portrayed as an old grumbling Cockney soldier with a walrus moustache.
  Old Bill moustache n., a moustache resembling that depicted on the cartoon character.
 
  1915 Bystander 3 4 Again, ‘Old Bill’ and ‘Our Bert’ and ‘Alf’, seriously comical and comically serious, fill the pages with their humour. 1930 Daily Express 6 Oct. 4/4 An enormous mouth fringed all around with stiff hairy bristles, just like an ‘Old Bill’ moustache. 1933 B. BAIRNSFATHER Laughing through Orient i. 15 Old Bill who, for many years, has been so closely entwined with my existence. 1946 R.A.F. Jrnl. May 163 During the last war, Bruce Bairnsfather created ‘Old Bill’, a lovable grumbler, typifying the foot-slogger of the British Army in Flanders. 1973 Times 2 Nov. 13/7 The Old Bill moustache starts twitching. 1986 Dict. National Biogr. s.v. Clark, Frederick Le Gros, Those who knew him through science called him ‘Bill’a nickname bestowed in the war of 1914-18 because of a fancied resemblance to the cartoon character ‘Old Bill’. 1998 Dawn (Nexis) 30 Sept. 21 Mr. Parker was an amiable Yorkshire man with an ‘Old Bill’ moustache and plastered down hair.
 

    b. An old soldier, esp. one who resembles the cartoon character.
 
  1925 E. FRASER & J. GIBBONS Soldier & Sailor Words 213 Old Bill, a veteran. Any old Soldier; in particular one with a heavy, drooping moustache. (From Captain Bairnsfather's celebrated creation ‘Old Bill’). 1939 H. HODGE Cab, Sir? 54 Here comes Old Bill himself.
 

    2. Brit. slang.    a. A police officer.
 
  1958 F. NORMAN Bang to Rights 138 Two Old Bill's came up to me and told me they had a warrant for my arrest. 1967 Guardian 14 Mar. 8/6 He observed a couple of men supping nearby who looked suspiciously like plainclothes men. Coulson asked the landlord. ‘Oh no,’ he said, ‘they're drinking pints. Old Bills only drink halves.’ 1983 J. SULLIVAN Only Fools & Horses (1999) I. 3rd Ser. Episode 5. 171 Rodney. Yeah, he said he was an old mate! Del. He's not an old matehe's an Old Bill!
 

    b. Freq. with the. The police force; police officers collectively. Cf. BILL n.⁵
 
  1970 G. F. NEWMAN Sir, You Bastard viii. 272 Giving Old Bill a bung was still an offence, and there would have been no consideration for the information. 1976 New Statesman 12 Mar. 322/3 If they were caught at it when the Old Bill (police) staged one of their frequent raids then we would all be up on a charge of ‘maintaining a disorderly house’. 1993 R. LOWE & W. SHAW Travellers 37 Because it's a motor vehicle there's no way I can stop the Old Bill coming in at any time they want with or without a warrant. 2002 Independent 8 Mar. (Friday Review section) 1/2 There's a ring of Old Bill around the entrance. They're there to break up the mob.