UPDATE: looks to be a problem on the low-power side of the board (+ I'm an idiot).
Diver300 was right in saying "I would expect 230 V ac on the rectifier, although that may only be there when that part of the hob is running." - the working hob, when turned on to create current in the hobs themselves, does read 230V (actually 250V).
The problem seems to be that for the 'dead' hob, the relay is holding a few V between the switching contacts, which may be keeping the high power (230V) on. The working hob holds 0V between the switching contacts, until the hob is turned on!
Between GND and the contacts, I've noticed the 'dead' one holds 13V and 16V AC on the relay contacts. The working one holds 16V and 16V AC on the relay contacts (giving an open circuit)
So far, I've found that this 13V is also held on one side of a cap (next to the diode), one side of a a diode (D1) and on the one side of 2 transistors (T1 and T10). The cap and diode (D1) are above the relay (white rectangular block) in the 1st image and the transistors are at the bottom of the 2nd image.
I think I need to find what is causing that 13V!