This is there reply this evening.
I'll try to explain. The / folder that you are seeing within filezilla is your account's folder /home/user/public_html.
/ on filezilla - /home/user/public_html
/public_html on filezilla - /home/user/public_html/public_html
In order to view the website publicly, all the files should be within /home/user/public_html and you have correctly uploaded the files to /home/user/public_html as such you can view the site http://theremotedoctor.co.uk/
The public_html that you can view via FileZilla is pointing to the folder /home/user/public_html/public_html (empty) on your account.