Fair enough - I have to say that the photo seems to suggest that you're probably right.
If it's coming from below (or 'through the wall) do you know where it is coming from?
If it's coming from sockets circuit, there really ought to be a fused connection unit ('FCU') feeding it.
What circuit it is on - a lighting circuit or a sockets one?
Is this on the ground floor or an upper floor?
Does that switch operate both wall lights at present? Do you want/intend that it will operate your new spotlights?
If (as you say) you intend to get rid of the other wall light as well (and maybe also the switch), you'll have to go through similar exercise(s) as we've been discussing for the first light.
The ideal would be to find out where these cables are coming from, and deal with things from there.
As I said, if it's on a sockets circuit, there should really be an FCU. Is the switch you mention just a simple switch, or does it have a fuse? Are there any other FCUs (things with fuses, with or without a switch) anywhere nearby, maybe in the adjacent kitchen?
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