Hi Wes.
eUKhost will make every effort to have you move any existing hosting acounts to the eUKhost servers.
Providing your previous host is using cPanel, the transfer process is extremely easy, and can be done with a few clicks by the eUKhost support team.
You may wish to keep your domain name(s) with your previous hosting provider, and change the nameservers so that they point to the eUKhost servers - or you may wish to transfer them to eUKhost, (this may result in an additional yearly charge, but I believe that eUKhost offers a free domain with each package, so hopefully, this will include domain transfers aswell.)
To get your
web hosting account transfered, contact eUKhost via email on support [at] eukhost.com before purchasing any hosting package - as this will make the file transfers etc easier.
Let me know if you need any more help.