Moving wordpress to another hosting server

So i have a dilemma where I need to transfer a wordpress site on to a different hosting server. Problem is I cant get access to the current hosting server to do a copy and paste using ftp. I have access to the wp-admin and I’m looking at all the different ways to do a back up. I already have the db sql file backed up but how about the actual php/css files? What’s the beset method to copy everything over so i can get everything running without any problems..