Cooker - Fixed load. Overload not possible. An event of a short circuit would trip whatever rating the MCB is upstream.
Yes, and don't get me wrong -
I have posted exactly the same comment before (a good while ago), and was torn apart over it!
This is how the 'discussion' usually goes.
The other side mentions manufacturers instructions stating it should be protected by a 13A fuse; a 13A fuse would blow before a 32A breaker, potentially saving some damage to the components of the oven; etc.
...and rarely, examples on this forum have demonstrated that an oven with multiple elements could trip an MCB, when for example insulation between the wiring and case has melted, one elements supply could partially short when another element is still heating.
If you wanted to cover for every eventuality, then changing the flex from the (probably) 1.25mm2 to 4mm2 would definitely allow the cable to be protected from such an extrememely rare occurrence.
But then, you are not only cutting off the plug, you are swapping the cable and ignoring the MI, so surely a case for voiding the warranty!
Hence, the non-controversial solution, that won't raise questions from an errant EICR...
the simplest solution may be to fit a socket to the cooker outlet - a solution that everybody seems happy with!