I had this problem recently; I think my kettle have accidentally been turned on empty. The kettle has a safety for that, described as follows in the manual:
"The kettle is fitted with a safety device, which protects against overheating should the appliance be operated with insufficient water. If this occurs the kettle will stop heating. Switch 'Off' at the power
point and allow kettle to cool before refilling. The safety device will automatically reset when the kettle has cooled down."
Then they go on to tell you that there is an additional thermal cut-out, and if that is tripped, you have to send it back to Breville for servicing. However, it might not be that bad-- it wasn't in my case.
The heating connector and control is made by Otter, here's information that I was able to find about it on their website (Otter A1 and CS7 control and connector-- I think the kettle actually uses a CS4 connector, but the thermal cut out isn't described on that data sheet):
"The A1 control integrates to 360° cordless plug with element
dry boil protection. Two bimetals spring loaded against the
element surface make a fast response during dry boil. One
bimetal disconnects the live side of the electric circuit and the
other disconnects the neutral. A latch out function prevents
dry boil cycling. This automatically resets when the kettle or
jug is lifted from the cordless base."
So what does this mean to you? If you look at the bottom of the kettle jug, there is a circular indentation that slots into the base. There are two white plastic things which I believe are part of the "latch out" described above in Otter's documentation. If you see them sticking out, they may be stuck in position instead of resetting as they should. Use something like a pencil eraser to gently poke them so they unstick, then put the jug back on the base. That should cause them to retract, and at that point your kettle should work again.