Repository folder on file system must be owned or at last to have read/write permission by the same linux user that your svn or apache via web-dav is working on…
In my case it was:
$ chown -R www-data:www-data /svn/reponame
But in some other case, it might be different, like
$ chown -R someuser:somegroup /svn/reponame
So replace someuser:somegroup with proper values.