I cant tell from the picture, but if the end panels on the cupboards go all the way to the floor (ie no cupboard legs), then they might have screwed through the side of the cabinet into the end of the plinth.
Ikea and B&Q kitchens use a plastic clip that springs around the cupboard legs, older kitchens I've seen use screws through the end panels or plastic spring catches.
You might have to resort to brute force and ignorance.
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