Anyway, my thinking is as follows (with quite a bit borrowed from the commentry)
The heat generated in a cable is equal to P=I²r, thus the temperature goes up roughly in line with the square of the current (I'm assuming for the purposes of this, that rate at which heat can be got rid of remains the same, which probably isn't strictly correct), I'm also assuming as the regs do that a cable run at its tabulated rating for a length of time will be at 70degress (again not strictly true, the rateings allow for worst case purity of copper, worst way you could install it and still be within the bounts of the reference, for example method 3 gives the same rating for horzontal and vertical trunking...)
Anyway if you have a broken ring thats an overload of factor 32/27 = 1.185, if we square this and multiply it by the normal termperature rise of 40 (30 to 70) we get 1.40*40 = 56, add that to the 30 ambient and you get 86 degrees
Each rise of 8degrees above 70 halves the lifetime of PVC apparently, so we have cut the life of our cable down to a quater, the starting life is assumed to be 23 years carrying the normal 27A constantly 24/7 so our cable will carry 32A for over 5 years
constantly before it starts to crack, etc, and as we don't generally load our cables fully and leave it that way 24/7, it should last a lot longer (for example, if the cable is not overloaded, but carries full load for 8 hours everyday, it'll last 69 years)
This all breaks down at around 120 degrees, when the cores start melting through the PVC and it goes bang anyway
(which is still quite a way from the 451F/233C flashpoint even paper has)
Actually if you work backwards from 115 degrees, you see something slightly significant, 115-30 = is a rise of 85 degrees, 85/40 = 2.125 times the normal rise, square root of that gives you 1.457 overload factor...
So to summerise...small-ish overloads should just cause the lifetime of the cable to be reduced, large overloads should end up with a nasty smell, a loud bang and a blown fuse before it actually sets light to things in the majority of cases, I trying to see if this reflects what people generally find in the real world
*I haven't got round to buying it yet, but was reading this
http://www.iee.org/Publish/WireRegs/Commentary-UpdateApr04.pdf