I don't think it is 'his server' but his personal space on 123-reg.co.uk.
Most 'hosts' publish YOUR website. You FTP to a SPECIFIC folder on the web site via an FTP address that directs you to the proper folder on the host server. That company which OWNS the server PUBLISHES your FOLDER as an IP Address and you generally have an INDEX.HTML as the entry point to that folder, unless it is a pure FTP repository. Difference is WHICH port is used, 21h or 80h.
You update/change files by using FTP to put the new files (or delete one) to the host server.
You can have as many 'unique' web sites with different names on a host computer, such as the ones on 123-reg.co.uk, as you want and they are all independent. You will have to 'purchase' each one individually. I don't think most hosts will allow a master 'menu' where you would come into the host via a browser and see 2 or more companies you could select.
Does this help explain how it works or are you trying to do something different.
I suspect you are confusing Remote Desktop with possibly opening a web site with a browser OR an FTP site with an FTP client which allows you to delete/add files?
Remote desktop would allow you to RUN the remote computer from YOUR computer. That means execute programs as if you were sitting at the computer. Add/delete/move/edit almost any file on the computer as well, and I don't think a hosting company would allow this.