OK, you asked for tutoring, so here's where I get picky.
The Godfather I was set in the 1940s- you might remember that Michael has just gotten back from fighting in WW2 at the start of the film. Godfather 2 has some scenes in the WW I and 1920s era, but unless your players are Italian immigrants they aren't going to be too pertinent.
(Incidentally, for the Prohibition version of the Godfather, see "Once Upon A Time in America").
The movies DeClench listed are all from the 40s, though some of the source material (such as Hammet's books) were written in the 1920s. Movies in the 1920s were still silent (the first major sound film didn't come out until around 1928).
(Side note: Ramsey Campbell is indeed British, but didn't start writing until the fifties. Some of his early Cthulhu stories would work in just about any time period, though).
Ok, enough irritating pedantry from me, here's my advice-
You can't really get a grip on the "average" 1920s game because there isn't going to be one, just like there isn't any average lifestyle in any period in history. Movies and source material cited in other threads will mostly focus on Jazz age, Prohibition gangster settings, which was of course only one part of life at the time. It's certainly not something Lovecraft wanted to deal with, unless hinting that the suspicious foreigners might be involved in bootlegging.
My suggestion is to decide the theme of the game you want to run, and then use that theme to focus in on the period. Like I said, a lot of the materials out there deal with Prohibition and gangsters. This is fine if you're looking to run a kind of hardboiled campaign, but not so helpful for assembling a group of academic Lovecraftian seekers.
For Academia, the recent Miskatonic sourcebook put out by Chaosium is set in the 1920s (ignore the modern-looking student on the cover). It's naturally not set in London, but should give a pretty good idea of what schools were like back then. I haven't looked at it yet, myself, so I can't say for sure. There's also an older sourcebook available in PDF, I have no idea how they relate.
Slightly related, the best literature from the time to look into would probably be Hemmingway and Fitzgerald, both of whom wrote about world travelling and the new youth movements. Hemmingway focused more on the former, Fitzgerald on the latter. They might not have much in the way of helpful details for the settings, though- since they were writing for the people of their time, they wouldn't have had much reason to explain how things were, any more than we'd need to tell a contemporary audience how to get on the internet.
Oh, last thing- what CoC base books do you have? Both BRP and D20 had articles on what things were like in the 1920s. The last BRP I have is fifth edition, but it had a price guide, notes on life, and a section on forensic medicine (short summary: yes to blood typing, no to DNA). There were also several timelines, not just important events, but "fringe" events like missing ships or rains of fish.
That's about all I can think of for right now. Like I say, I think you'll have a better time focusing on an aspect of the period instead of trying to absorb everything you can find. Talk it over with your players, too- it's likely they have conceptions about playing a historical game that will help narrow things down.
