As you have hot water pumping through it can't be the pump so it must or usually is caused by air-lock.
Try what I did Blow hard down the tap spout in kitchen sink with cold tap in open position see what happens.
The other thing to try if you have an in-line pressure switch. This will be in the cold feed pipe on inside under seat at water pump unit entry position. It's White looks like a stop tap. Turn the knob on top clockwise to close the switch down. Turn on the kitchen sink COLD tap then turn the knob on the switch anit-clockwisse untill you hear it 'Clicking' then stop turning the knob. Hopefuly by this time water should be running out of the kitchen tap now leave that running and turn on the basin tap to get that flowing. Can't think of anything elses except tap micro swtiches on the taps but can't see two going at same time.
