HTTrack Website Copier might be just the tool for you, especially if you don’t have FTP access to the old site…
As the site itself says:
“It allows you to download a World Wide Web site from the Internet to a local directory, building recursively all directories, getting HTML, images, and other files from the server to your computer. HTTrack arranges the original site’s relative link-structure.”
Pretty impressive!
Happy copying,
Atg