Taps either have screw down valves or ceramic disks and a certain level of water pressure is required to make it work. You need to find out from the retailer what is minimum water pressure required.
You then should measure the water pressure or estimate that. If you have the right pressure for the tap and it still fails to work then you could have a restictor on the tap or something else blocking flow.
With a plumber's help you can always remove the tap and see if water comes out, that will determine that the fault is with the tap and not the pipe system.
First of all, go to the retailer of the tap, and if an old tap, go to the manufacturer. If you do not know the manufacturer name, you will probably need a plumber, or to buy a new mixer. Mixers can cost only 10 pounds from lines like Amber.
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