The recommendations are any fixed item over 2kw is supplied other than the ring main. Although an oven and even some of the domino hobs could be supplied from a 13A socket that socket would not normally be part of the ring main.
Manufactures often stipulate the max and min size of protective devices and if we consider a cooker supply of 32A this may be enough for both and it is common to fit both oven and hob from same supply.
However some hobs need a 45A supply for hob alone and 16A for an oven is also not unknown. Yet my stand alone hob and oven is designed to run on 32A even though just one ring can draw 15A. There is some circuitry which limits total yet still allows individual rings to draw 2.4kw, 3.0kw, 3.0kw, and 3.6Kw and the main oven has top, bottom and rear elements which can be selected giving normal and fan and even a fan grill so can draw 6kw. And top oven another 4kw which all adds up to well over 32A but clever electronics prevent total overload.
So what I am saying is without having the manufactures recommendations it is impossible to answer your question.
Still lacking info for will try to answer.
Unless the hob is induction worse case scenario is the 32A MCB which normally supplies the range of cooking utilities will trip. So adding too much to a circuit is normally not a problem.
However with induction then losing power also means losing fans and cooling so with induction not really something one wants to happen.
40% over rating and hoping diversity will allow is common but with 30A + 2 x 13A = 56A on a 32A MCB is going a little OTT.
Having said that likely it would work without a problem as normally not all items used together. Even if all switched on together the thermostats likely will mean not all drawing current together.
But you have not said what the supply is? And at the end of the day it is down to guy signing the paperwork as to what he thinks is acceptable.
This work will unless in Scotland be Part P controlled and each electrician or LABC inspector will have their own ideas and it is down to them what they think is acceptable.