All right...so. As usual, take my suggestions with a pinch of salt. (Is "pinch of salt" a peculiarly British phrase?)
Page 1:
"Baker Street", not "Baker's Street". Troy! Honestly!
"Detective committee" sounds a bit modern. "Investigation committee", perhaps, or something.
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"Police clearance" and "Law enforcement authority" is a bit modern too. Perhaps something a bit more vague and English? "There is a gentleman's agreement that these committees have a similar authority to the Police when on a case.", say.
"Suburb" of London is a modern phrase. "Borough of London" would be good.
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There's no copyright ministry. For this, it sounds as though instead of "Bureaucrat" you want to say "Civil servant". The Treasury collects taxes, so how about "Perhaps he worked at the Treasury, collecting taxes" or something similar?
Under Historian, "College degree" should be "University degree".
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A Professor in England is a very highly ranked college lecturer (not all college lecturers are professors). It sounds as though you want something more low-key. "College tutor"?
Page 5:
"the British Army" rather than "Her Majesty's Royal Army"
"Elementary or secondary teacher" is a good British phrase but too modern. Perhaps just "Your character was a schoolteacher" or "schoolmaster".
Page 6:
"the Houses of Parliament" not "the Parliament Building". I think you know this from the way you've written it, but Big Ben is used both informally to refer to the clock tower and (correctly) to refer to the bell within the clock tower.
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I think "Fence" is a slang British term for someone who sells on stolen goods, not anything you'd see on a shop sign. This may not matter to you if "Ignacio's Fence of Curiosities" is a tongue-in-cheek name. But perhaps "Ignacio's Emporium of Curiosities" or just "Ignacio's Shop of Curiosities" .
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Homicide is an American word: it's "murder" here. Child worker, probably, rather than Child Labourer.
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Probably "stabbed" rather than "knifed".
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The weather description is quite good. "Smog" is a bit too modern, but London's fog was legendary. (A heavy fog was known as a "pea souper", because it had the consistency of pea soup). It's not bitterly cold in the winter: it's just rather dank and rainy all year.
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Was there actually a Swansea or Ulster Railway Station? If you want a real name, you could use Waterloo or St Pancras.
"Hound and Tails" isn't a common British pub name (although perhaps you got that from the original stories). If you want a common name, how about "Horse and Hounds"?
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I'd say just "Poker" rather than "Fireplace poker", personally. A "Rugby Club" is generally used to refer to a team of men who play rugby. Or you might be making a joke, actually, I'm not sure.
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Just "soldier", not "royal soldier".
"Blackmail", not "extortion".
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"Bobbies" is a bit too informal: a "bobby" is usually a policeman on the beat not a Scotland Yard detective. Not sure what to suggest here except for "Detectives" or "Police".
The British phrase (if you want to use it) would be "got off" rather than "gotten off". British people don't say "gotten".
200 British pounds is a huge amount in those days. I'd say rank times 10 or 20.
And, just as a suggestion, you could always run your text through a UK English spell checker to put the whole thing into British English.
That was fun!
Graham