DIAGNOSIS The seal between the stainless steel inner wall and the plastic base of the carafe has likely failed. It's a known weak point on this model.
FIX Unfortunately, this isn't user-serviceable. You'll need to contact Breville customer support directly. They are often aware of this issue with the BDC455 carafes and may offer a replacement under warranty or for a reduced cost.
IF THAT DIDN'T WORK While waiting for a new carafe, you can try using the machine with a standard glass carafe (like from an older drip machine) on the hot plate setting, but you'll lose the thermal benefits.
HEADS UP Don't try to seal it with epoxy or food-safe silicone. High heat and coffee oils will break it down, and you risk contaminating your brew.