Phantom Studs

Hi all, I'm a DIYer trying to mount a shelf in my kitchen, but I can't find the studs. The kitchen itself is a cavity wall extension on an old, terraced solid wall house. There are four heavy cabinets mounted high on the same wall, and I want to put the shelf in below the cabinets but above the radiator.
To find the studs, I've been drilling pilot holes, using magnets, and tapping the wall to hear sound differences. I don't have a stud finder. The magnet sticks to the wall a few cm above...

Phantom Studs