My bath taps are combined hot and cold. The cold tap is slow running even when fully turned on and sometimes runs to a trickle. I have attempted to strip the tap down which appears to do the trick only for the water to run slow again as time goes by.

Gerard Garner, December 2010

Difficult to say with out seeing them, but if the cold is tank fed then it could be air locked. You can try placing a hose pipe from your basin cold tap onto the mixer tap, (you may have to warm the ends to make them fit) open the mixer cold first (keep the hot side closed) and then open the basin cold tap. The pressure usually forces air out of the pipe. Do this for two minutes and see if it works. If the taps are cold mains fed then they are knackered and need replacing.

Pete the Plumber., December 2010