We getting into exam questions here?
Most probably, nothing.
The cable rating depends upon exactly where it is run....how much it can dissipate heat. As long as it does not actually run through insulation it is probably ok to carry 20-25 A. Above this it will heat and the insulation will slowly degrade.
What you (may) have is a ring divided in half, each half rated to carry 20 or more amps. There is only 32 A available altogether, so there is a reasonable chance that:
1) the circuit never actually got near its 32A limit so never overloaded anything
2) Even if it ever got seriously going, the load was divided between the two parts so neither exceeded its rating.
3) even if it did, circuits are designed for occasional overloads.
The most likely place for a problem would be the kitchen, if everything was on the same half of the ring.
However, If the ring is only broken in one conductor, then return current would still be using a ring. Which would increase the effective cable capacity to around the full 32A mark.
Oh, and you are planning to add another 13A load. Guess that means you reckon there is spare capacity out of the 32A . Most probably a good bet, but I would recomend a separate kitchen ring when someone has the choice.