My girlfriend has the wrong assumptions about me and is not ready to believe that I am not at fault in anyway apart from my mistakes that I have apologized to! How do I make her believe?

Then time has come for the parting of the ways especially if this is how she feels about you. You may be being set up here and this is how shes breaking up with you, I don't know but you two have reached a brick wall with neither willing to give so best just to pick up the pieces and end it the best you can and just move on here.  Sorry and good luck