This site also has very short stories with vocabulary and comprehension questions: http://www.rong-chang.com/qa2/

Shirley Jackson's short stories are also good. Here's one I like: 

https://www.loa.org/images/pdf/Jackson_Charles.pdf

Let me know if it's too difficult for you and I can try to find something easier.

You might want to start with Grimm's Fairy tales. As a kid I hugely enjoyed Enid Blyton. You could later progress to Conan Doyle, P.G. Wodehouse, G.K. Chesterton's "Father Brown" series. The apex would probably be Bertrand Russell's short essays. These are all "English" English though, not the "American" U.S. variant.

Basil, one of the things that is sadly lacking on this site is the ability to edit.

"Aesop's fables" at the start. Why do I not see a way to edit my earlier comments?