Penguin's New Writing Magazine was established in 1940. The original magazine was in the original series run of Penguins but then became its own magazine. There are a periodical with several stories in their pages and developed by John Lehmann. They are a lovely little magazine and famous authors of the time contributed to them including George Orwell.
I have the following list in my collection but am always looking for more of them to complete the series. The last issue was published in 1950.