OP, sounds like we have similar taste in books! Here are some I enjoyed that you might like:
Wintering - Derek Johns (set in the 50s, so a bit later than you wanted, but it's so well written, quite simple, about a family, quite short, really worth reading).
If you like crime, Laura Wilson's books about a detective in London (Ted Stratton) are really good and set in the second world war and 50s. Very atmospheric.
Another crime/1950s one that I absolutely loved was A Commonplace Killing, Sian Busby.
The Lie, Helen Dunmore, set just after the first world war, about... a lie! Can't say more or it'll give away the plot but really good. I really like all her books that I've read. The Greatcoat by Helen Dunmore is good too - it's slightly supernatural but not scary or anything.
Dead Man's Embers, Mari Strachan, set just after WWI, a family in Wales coping with a shell-shocked husband.
In the Dark, Deborah Moggach - loved this one, about a family after WWI, so well written.
Spies - Michael Frayn, set just after WW2, about two little boys who are on the trail of 'spy'. That makes it sound childish but it's not at all, really good story.
Alone in Berlin - Hans Fallada - not strictly historical fiction as it I think it was written at the time it was set (just after maybe? not sure) - about a couple who are against the Nazi regime. Really really good.
Painter of Silence - Georgina Harding - set in 1950s Romania, about a deaf and mute man. Very interesting as I knew nothing about Romania in this period, and very good story.
My descriptions are rubbish, sorry - just didn't want to give away too much (o: Hope the ideas are some help.