Remember that during this period "British" people spoke in different dialects depending not only on where they lived, but on their occupation/social class/education as well. So the answer is going to vary depending on what kind of young people you're asking about.

At any rate, "Hi" actually was used quite a lot during this period, but not to signify "hello" so much as "hey" (in a I'm-trying-to-get-your-attention way). So instead of calling "hey, Jack" if you were trying to get Jack's attention, you'd say "Hi, Jack!" See here for an example of that usage, which is very common in British literature from this period.

In terms of what a standard "hi" type greeting was among young people, I'm not a linguist or anything but I've read a lot of british literature from this period - and to me it seems that "hello" was actually the standard greeting - with variants like "hullo" and 'allo being more common amongst different social classes. I certainly can't think of anything that would even begin to rival those as a "standard" greeting.

I flipped through my books and the only thing I found was in Code of the Woosters (1938) where we have:

Bertie Wooster: Oh, what ho, Sir Watkyn!
Sir Watkyn Bassett: Kindly do not address me in that familiar way, Wooster.

He also addresses Aunt Dahlia the same way in Comrade Bingo (1922).

It is not always clear whether Bertie Wooster's speech patterns represent typical speech of an upperclass numbskull, or just a meandering tendency to say whatever pops to mind.

You might also try in /r/linguistics.

To add on to this, did 'Trans-Atlantic' English see a different variant of greeting than the greetings of the 20s-50s? Was it more formal, as in a 'Hello, how are you today' manner?

This is a question which has a very simple answer: "Hello".

Can I just point out that a lot of British people don't even say "hi" now. It's pretty rare in a lot of places, and seen as an Americanism.

The usual greeting is "Alright?" which must be at least as old as the 30's-40's.

So the simple answer to this is "hello" for the middle and upper classes and "alright mate" for the working classes. Or, as someone else says "wotcha".

But the even simpler answer is "hello/hullo/'allo" for all classes.

Or "ayup" if they're from the north. Yorkshire, etc.

My father was from that place and time. His standard greeting was to thrust out his hand, look the person in the eye and say "How do you do?". Or, as it came out: "How dyoo do?". I believe this was fairly common. Street slang from the time that I have gleaned from literature varied wildly from place to place. "Wotcha!" was one such (highly informal) greeting.

Additional question which might be relevant: a greeting like "Hey" is used in Sweden. Does "Hi" and "Hey" in English come from Scandinavian input in mediaeval times?

Google ngram suggests that in literature at least, "hello" was relatively common by the 40s, but not as common as today. Interestingly, "what ho" peaked around the 1860s, so perhaps it was real slang at that period or a little earlier. "Halloo" was also more popular at that time, but it may have not been used as a greeting. I didn't include "hi" in the graph as another commenter points out it had a different meaning, and it dominates the other terms.