I was working with a designer and he placed my site here - http://markonefs.co.uk/new/ I have lost contact with him and want to download the site and its content to place on a new server to which I will redirect my domain. I know it was build in wordpress and I might not be able to retain the use of it with wordpress. Should I just scrape the source code for each page and reupload pages to a new server?
That depends on what type of site it is. If its all html you can use httrack to copy the site for you to your computer, which you can then upload to your new server. If its php or asp then you're out of luck, as these are all done on the server then sent to the browser, so you could never get the source code without ftp/ssh access to the server. As its wordpress you could get some of the template but you would have a lot of editing to do to get it back to a working state
No, you shouldn't as you'll get really awful result. Wordpress isn't that vulnerable that everyone can just copy paste source code and make own template or content. Anyway if that site is already hosted then you are duplicating it.
You can do this work in 2 way: 1. Login to your C-Panet then go FileManager-->public_HTML and then download all the files one by on OR 2. Use fileZilla. download FileZilla and install it first. Then login and and look at middle right position. You will see FileName, click on public_HTML and wait, after few second list of all the pages will be listed in the same position. Just select all and right click on them--> click on Download your work is done now. now upload these in your new server.