That's not how it works
Yes, the ring was a solution to a copper shortage. However, as was stated above, the fuses in the plug protect the appliance's cable.
The fuse (or more likely these days, the breaker) supplying the ring protects the ring itself from overload.
Rings are normally rated at 32A - it doesn't take many moderate loads (say 3A) to overload a ring, which can easily have 10 double outlets on it (there is no restriction on the number of outlets).
However, there are further complications as unequal loading of a ring can theoretically lead to an overload if it is fully loaded at one point that is near to the origin - the load is effectively shared over two cables that may have significantly different resistance, so one will take more current than the other.