It is the second – italic – paragraph what I always forget. Thanks Mark Embling!
To move a file or set of files using tortoise, right-click-and-drag the target files to their destination and release the right mouse button. The popup menu will have a ‘SVN move versioned files here’ option.
Note that the destination folder must have already been added to the repository for the ‘SVN move versioned files here’ option to appear.