I found that if the projects that are related with the SVN you are trying to relocate are open in Eclipse, the operation fails with the following error in the 'SVN Console':
switch --relocate http://old.scm.com/svn/APP http://new.scm.com/svn/APP .../webapp
svn: E155019: Cannot relocate '...\webapp' as it is not the root of a working copy
svn: E155019: Cannot relocate '...\webapp' as it is not the root of a working copy
The solution was to close all the projects (Project Explorer -> right click on the project -> Close Project) and only after that, do the URL relocation in the SVN window (SVN Repositories window -> right click on the URL of the old SVN -> Relocate).
Notice that that the box 'Projects that will be relocated:' on the following screen is empty. Before it showed all the open projects in Eclipse IDE.
This was they only way I got it to succeed.
Using Eclipse Kepler Service Release 2, with Subclipse 1.10.10.