No, it’s not.
In fact, the most cursory knowledge of history and of current events informs that believing and preaching the Gospel is a good way to get killed or at least blackballed. Anyone who preaches the Gospel and insists on the orthodox preaching of the Gospel by clergy has a snowball's chance of becoming a bishop in today’s Church of England, token flying bishops excepted . . . for now.
To be fair, Sarah Mullally was referring to churches safeguarding the young and vulnerable from abuse. Certainly, churches have important roles to play in that regard. But is safeguarding “at the heart of the Gospel”?