your cold water taps ,and other cold outlets like toilets /washing machines etc, can be connected directly to the mains supply , or if you have a loft tank ( cold water storage cistern) As you have ,they can be supplied from there. however the kitchen sink cold tap is never from storage and is always directly from the mains. some propertys have a mixture , some things off mains and others from tank. I have no idea what your set up is. but given the fact that your mains appears to be on and loft tank is being supplied ,any cold tap / other outlet connected to mains would be giving you water ,( unless an isolating valve to the individual tap / outlet is off ). you do not get airlocks on mains .so I am drawing the conclusion that those cold taps / outlets that are not giving you water ,are not connected to mains ,but are fed from loft tank .as you have given no indication that you have turned off any other valves relating to the loft tank OUTLET pipework ,then an airlock is suspected. not being there I can't be certain ,but on the info you have supplied it seems likely. if you have a look at the bottom of your loft tank you should see the outlet pipes ,I suspect you have two ,take pics and post back.regards terry