This problem has only started to happen after an automatic XB1 update which installed on 3/1/15.
After that point no saved games will load.
After selecting the Saved Game to load it gets to the next screen where the rotating object is shown and then after a few seconds it freezes with a buzzing noise. It then throws you out to the Xbox One home screen.
I have done a restart, a full console reset, and a full game uninstall/reinstall as per the crashing http://www.gamesas.com/topic/1543740-fallout-4-xbox-one-support/, but the problem still exists.
Any suggestions for a fix, or is this now an incompatibility with the XB1 update?