One or two things Paul,
One, If it is an old house, it could be the pipe is frozen either in the wall or in the loft. If the tap is tank fed, then check the tank to see if there is water in it and that the ball valve is operating and not stuck (gently move it up and down.) If the valve hasnt stuck then it maybe the cold feed to the tank is frozen and at that point beware of a burst when it thaws. Find where your stop tap is and turn it off before bed and before going out to prevent a flood.
two, The mechanism in the tap is broken and the washer is not lifting off the seat inside the tap, either repair or new pair of taps.
Plumbo
December 2010