Media Problem after replacing old site within existing Server

I would appreciate some help with Media on my new site which has just gone live.
I created the site from a purchased Theme and over the last month have been updating text and pictures. Fantastic as this is my first site.
The new site was on my existing ISP’s Server in a folder as ‘newsite’ with the url: http://www.idcardservices.co.uk/newsite
I asked my ISP how to remove the old site and install the new site, instructions as follows.
On the day of moving, via FTP in public_html, I created a new folder ‘oldsite’. and put all the old site into the folder.
Once done I opened my ‘new site’ folder and put all the contents into public_html
In General settings I changed WordPress Address (URL) & Site Address by removing ‘newsite’
Everything seems to work well and I have tested it in all the Browsers, pages are there, sliders work email form works, images are present etc.

But, in my Media folder in wp-admin most of the pictures listed are unattached.
When I upload a new picture it seems to upload the image but cannot be viewed and I get a broken link box on the actual web page.
I now know that there was a better way of moving the WP site but did not see that at the time.

This is my first site and I have very little technical knowledge and reading the WP support forum has only confused me more.
I don’t want to lose the images I have on the site already but need to upload many more and cannot do it.
Thanks
MrB