Thanks for your help so far guys
Jem, Not wanting to sound too dim here
, So I could build the new site on a spare / unused server I have at the moment, with use of Joomlapack to back up the site and upload to the client server when ready.
Also, in this case, I have suggested the client create a new account with my host company (His current host isn't very good) So I will be making the transfer to this new host with the client changing his DNS settings at the final stage, does this sound right?