I have discovered that if I use the rear window heater to clear ice or demist the window that the DAB signal disappears and the radio is silent until I switch the heater off again. All other bands are fine.

Plugging the VCDS in shows that there is a fault found on the digital radio antenna, code is B1103 11 [00001001] - short to ground.

Does this mean that the rear heater element also doubles as the DAB antenna?

If so, then does that mean there is or should be a decoupling capacitor between the radio and the element to isolate the DC voltage when the heater is switched on from the radio input, while still allowing the AC radio signal to pass? If so, where is this decoupling capacitor located?

Check:

1) if there is a broken wire in the cable guides to the tailgate

2) the antenna amplifier could also be defective

The rear window heater has a dual function: radio antenna + heater. This can explain what you see.

I would dig as @Cairus proposed.