That is true for hobs with resistive elements. Induction hobs have switched mode power supplies and will take the current they need for the wattage provided the voltage is within the range specified.
Since you have given the sizes as 7.5kW plus 1kw then there unlikely any problem.
Having used an induction hob what ever the power rating over the cooking time power will be much less than with any other electric hob. It's simple maths heat into the food is same with any hob and the induction does not heat the room only the food so it must use less power than any other type of hob.
Cables do no heat up quickly they heat up over some time so unless ludicrously thin then it is the average power used over say 1/2 hour that is important not the instantaneous power used on switch on.
There are always exceptions to the rule. There are hobs designed to time share and only use 3kW and replacing that type with a non time sharing hob could cause an overload but in the main under normal use an induction hob will use less energy than any other hob.
The standard supply for a kitchen for the cooker will take 32A and will run both hob and oven. Only when the supply has been de-rated is there a problem. I have seen where the supply has been extended using under size cable and other factors can de-rate the cable. But the last cooker could have been supplies incorrectly so comparing old to new does not tell you it's OK.
For a very short time I was employed to fit cookers and left because the firm would not supply me with the test gear required. They wanted me to pay for my own at £750 a set.
It does not matter what anyone says on here what is important is the actual installation and only way is to visit and test and inspect to be 100% sure. From what you have said I am 75% sure it's OK. But if you want 100% it must be tested.
In the same way as the firm would not give me test gear the same applies for many others and pre-2004 there was a lazy-fair attitude to replacing cookers and the like with little or no testing. Although Part P improved the situation it is still true that items are fitted without testing the installation supplying them both DIY and firms.
In theroy there should be an installation certificate, minor works certificate, periodic inspection report, or an electrical installation condition report which the installer should check before fitting new appliance. However in real terms these are often missing. Clearly plugging into a 13A socket we don't check the wiring first and with a cooker outlet marked as such often it is taken for granted in the same way that is can supply 32A.
One would hope major firms test before fitting but I was working for a major firm when I was not supplied with test gear. I would love to hear what others say but in the main it's down to trust and you need an electrician you can trust to test the installation you will not have the equipment to DIY the testing.
So you have to make a risk assessment. Fit the new without testing likely it will be OK but it's a chance. Or employ some one to inspect and test and be 100% sure.
That is true for hobs with resistive elements. Induction hobs have switched mode power supplies and will take the current they need for the wattage provided the voltage is within the range specified.
That presumably is only true if the power supply is fairly well regulated. Given that the input voltage range specified for induction hobs is pretty narrow (IIIRC, virtually all I've seen have been "220V-240V"), I'm not convinced that there will be necessarily be particularly tight (if any) regulation - and, if not, it would probably behave essentially as a 'dumb/passive load', not dissimilar from a resistive one.
In fact, I'm not sure what these power ratings actually mean. Given that the primary determinant of power consumed will presumably be the characteristics of the cooking pot (essentially the impedance of the eddy current loop in the pan), I might suspect that the quoted figures probably relate to maxima imposed by control circuitry - but I haven't a clue as to whether that is actually the case!
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