'\' is not a working copy.
Downloading and testing the latest SVN command-line client yielded much the same results, only with some different messages.
After much googling I got a sneaky suspicion that there was an issue with my working-copy actually being on the root of a drive; in my case U:.
Checking everything out again, but this time at U:\wc worked perfectly.
- TortoiseSVN 1.6.10, Build 19898 - 64 Bit
- Subversion 1.6.12
To sum it up: Don't upgrade if you have your working copy at the root of a drive and it is currently working!