Double Socket Not Working (UK)
Mains tester screwdrivers are useless, dangerous and should be thrown away. They rely on current passing through a neon, resistor and your body and if they are faulty or they get wet they can kill you. They give false positives and negatives. 

Check that all wires are done up tightly in the socket and that the terminal screw isn't gripping the plastic insulation on the wire. And check at the kitchen socket it's spurred from too. It's possible the neutral is out, but the live is connected, or vice versa.