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It’s kinda hard to say without having a look.
Literally went and looked at a very similar situation in my mates place the other day - needing a supply for a 30a induction hob.The good news is that you have a proper cooker switch there, and a cooker circuit on your board (according to the EICR), so I’d assume that you have a sufficient supply cable to that cooker switch and socket, so should be pretty straightforward for the spark to sort out (providing that all is expected with regards to cabling).
I forgot to link to previous post which had it attached.
I won't spam it again but you can see it here...
https://www.lfgss.com/comments/16278337/
i think the double socket in the alcove (on left side) was probably where the cooker control outlet was located and like you said was replaced to facilitate a hob (the bit of wood on the left also looks like a remnant of that). there's nothing on the right hand wall inside the chimney (i was sure i'd find one there when we went to measure up).
I've ordered a 30A cooker to be installed on 16th dec from AO, we get the keys on the 11th, will get a sparky in to take a look and if need be fix it before the oven arrives.