Google found this thread which suggests the ring and oven faults might be related...
http://www.howtomendit.com/answers.php?id=267630and also this post..
http://www.amazon.co.uk/Belling-WHITE-electric-cooker-separate/dp/B0000C789V Quote:Just a brief word of warning to anyone thinking of buying any 335 Belling cooker - I have barely had this cooker two months and, despite it being perfectly maintained and looked after, it has broken down TWICE already. First time the one hob and the oven stopped working - it was due to a "common problem", where the thermal switch inside the cooker cuts out due to the oven having a fault where it sometimes fails to switch off at the correct temperature, so I am told. Second time, the front hob stopped working, which is therefore due to a different problem..continues
That sounds like a faulty thermostat trips a thermal fuse.