Then you would need your head of year to write to them, not you.
If I tell you that my head of year said I'd get AAAA in my A Levels, how do you know if I'm telling the truth or not?
^^^ This
how could your school get your predicted grades wrong?
having looked at the application form ... you were supposed to fill in the predicted grades yourself and simply have your school confirm that they were correct as part of their reference