Flexible LED strip lighting for the kitchen from Hafele https://jhauto.en.alibaba.com/product/60541497048-212056234/White_PCB_5M_600_LEDs_Flexible_LED_Strip_Waterproof_IP65_RGB_Tape_Light_Decoration_For_Holiday.html
4m IP65 Waterproof LED Tape Kit - Cool White/Warm White. I think this would be the simplest product to house underneath the shelving. The complicated bit would be figuring out how to continue it under the cooker hood. Also I am not sure what level of light would be produced and therefore how good this would be for task lighting. I will send some sketches for possible options for how to house this lighting strip this evening.
How to Buy and Install LED Tape (Reviews/Ratings/Prices)