Use wget in this manner (m for mirroring):
wget -m ftp://username:password@ip.of.old.host
If your username or password contains special characters, you may need to use the format:
wget -m --user=username --password=password ftp://ip.of.old.host
Alternatively, I found this guide which shows you how to do it using ncftp in Debian. You will require root access to the new server if ncftp is not installed already.
In short:
sudo apt-get install ncftp
ncftpget –T –R –v –u "ftpuser" ftp.nixcraft.net /home/vivek/backup /www-data