Second, consider getting a critique before you decide whether you need to pay for a full copyedit. I (and probably many other editors) will read your manuscript and write a several-page critique for much less than the cost of a line-by-line edit, and if your mechanical skills are reasonably good, this may be sufficient to help you get it into adequate shape for your publication plans.
EFA has an excellent reputation in the field, and their high annual membership fee keeps out the riff-raff and newbies merely flirting with the profession. For writers, EFA also has a very useful rates survey for the different kinds of editing, helpful for anyone shopping around: (the-efa.org/res/rates.php) For those keen to find a fully vetted editor, try Editcetera (editcetera.com). This group not only tests every applicant, they also supervise for a full year. Of course, their rates are higher. Another highly regarded editorial organization is Bay Area Editors Forum (editorsforum.org), with a searchable database of editors. I’m a member there.… Read more »
That said, I don’t recommend going to publication, particularly if your book is intended as a revenue-generating venture or as a vehicle of professional promotion, without making sure that someone with an eye for detail has gone through the entire manuscript and ruthlessly noted every typo, every spelling error, every misplaced comma, and every ambiguous sentence.
Start with a google search and see what comes up. Click on a handful of options and see if you can find an editor who is specialized or who has edited books similar to your own. An easy way to do this is to open just a few of your favorites in tabs and check out each editors’ website and about me section. Take a look at their testimonials. See if any stand out to you.
Some authors budget very unrealistically, perhaps just a couple hundred dollars. (I’m not saying this is necessarily true in your case, but I have encountered it.) In such cases, I find myself wondering whom they are imagining should bridge the gap between what they are comfortable paying and what the editor needs to earn in order to pay expenses and support him- or herself.
If neither Sally nor myself feels quite right for you, then I suggest you browse the bookstore or even the public library for books published in the last few years that remind you in some way of yours. Check the Acknowledgments page to see if they thank an editor. If not, see if there is any information to contact the author and ask if they used a freelance editor and if so, would they recommend them.
I’d add that for UK writers, the Society for Editors and Proofreaders (SfEP) Directory is the best place to search for editorial professionals. Each editor has been vetted for professional competence through the Society (you have to be assessed to become a Professional Member or Advanced Professional Member), so it’s a pretty trustworthy source: http://www.sfep.org.uk/directory/directory.asp
I cannot speak for all editors, of course, but I know I and many of us would be open to editing just part of your book at first, say, a particular chapter or two that you sense needs a lot of work. That is often enough to show you mechanical errors that you tend to make repeatedly. You can then go through the entire manuscript yourself looking for as many of the same kind of errors as possible. You will sharpen your basic writing skills in the process, and it will pay off in all future projects.