Crime Stories

Who are the best publishers to approach with a view to publishing crime fiction short stories/novels?

It Might be best to approach a writers agency first they can give you the best advice regarding publishers and contracts or try contacting the publishers of similar books you have enjoyed
Buy the Writer's Handbook, (this year due out Jul), or the Writers' & Artists' Yearbook for a list of publishers. It will explain who will publish what and how to send your mss.
Check out chapteread.com - it's a writing site and they explain everything - there is a link called the "publishing process" and it's at the top of the site -- can't miss it!