Backup options for user disabled on Host

Looking to find a way to make a backup copy of my website and I will explain in brief detail my problem. I am using CPanel because it had all the features I needed but I did not realize that my hosting service had removed some of the features that made me want use the program in the first place like the backup button and the backup wizard button. Now I am trying to get them to supply a full backup of my website which is not easy! My question is are there any other ways of making a full backup of the website such as plug-ins or something like Acronis without getting the hosts permissions first because I am afraid they may become even harder to deal with. I have tried changing hosting services once already but they were not able to make a full backup of my website so I was forced to stay with my old hosting company. Without the backup buttons in Cpanel to make full backups on a weekly basis I am being held hostage right now. Thanks for any advice or ideas you can offer. Jim