The term, "Wooden tops" seems to predate World War 2, at least in military terms. It was a derogatory name for the Guards regiments in the British army, some of which emphasised drill, display and ceremonial etiquette to the exclusion of all other military skills.

(It may simply have been a reflection on their over-disciplined love of spit and polish, or it might have referred to their resemblance when on parade to a row of skittles in a bowling alley, but I am guessing here.)

It doesn't seem to have crept into criminal slang to refer to the Police until the 1960s, at least as far as I know. It occasionally cropped up in the series "Z Cars", which was shown on British television in that decade. In this instance, it might well have been adopted from the childrens' television programme of that name. It might also refer to the preference of some policemen for the letter of the law to common sense.

Accepted slang names for the Police in detective fiction prior to 1960 included: "Peelers", "Bobbies", "Rozzers" (references to the Home Secretary, Sir Robert Peel, who established the first Police forces in the 1840s); "Busies", "Filth" (pronounced in Cockney as, "Filf"); "Scuffers", "Plods" (both of which might refer to the heavy-duty footwear they usually wore); "Old Bill" (possibly a reference to their common duties at the Central London Criminal Courts, which was / is known as the Old Bailey).

Also, "Boys in Blue". Some crime novels e.g. Tom Barling's "The Smoke", set in the 1960s, have members of the CID (Detective branch) referring to the uniformed branch as "serge", from the material used to make the uniforms.

Current TV drama series featuring the police, such as the long-running, "The Bill", has detectives usually just saying "uniform", e.g. "Uniform have just attended another off-licence break-in, looks like your suspect again".