I'm using LFTP (
http://lftp.yar.ru/) with Linux and it works fine. Here is an example from the shell script this is from. I run this from crontab.
I have it deleting the uncompressed backupfile that i get when I backup my DB using mysqldump but you can have it delete anything you want.
The $mdate puts the current timestamp on my files (which it gets earlier in the script).
If you plan on using lftp make sure /usr/local/bin is in your path and its exported.
lftp <<EOF
open yourftpserverhere
user USERNAME PASSWORD
pwd
put dbname-$mydate.tar.gz
bye
EOF
rm /dir1/dir2/dir3/dir4/backup.sql