The simple answer is NO. The items on your 15mm copper pipes are on the left a compression pipe connector. On the right is a Double Check Valve, that is probably connected to the cold tap. This pipe will be mains fed meaning the water will be directly fed from the cold entering the house. You may or not have a cold water tank in the loft if a house. To work on the kitchen sink taps turn off the cold and hot water by turning the two outlet pipes that leave the bottom of the cold tank, if you have one. The hot tank if you have one will not empty because the water should leave the hot tank from the top, but remember to turn off the cold supply to the hot tank first. You can turn off the mains cold from the Stopcock or by the water meter in the street if you have one. If not you may struggle to turn off this tap and so will need to ask your water supplier to check its serviceability as you will have problems if you need to stop the stopcock in the house from dripping or if too stiff to turn.
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