Several possibilities here:
Frozen pipes or at least restricted with ice? Try pipe insulation if it's cold. If it's not cold then obviously it's something else.
A leak somewhere in the supply pipe? Trace the pipe back to a supply pipe you know gives a good feed, and fix any leaks.
Try turning the tap further open in the cistern? Tap may not be fully open, thus restricting the flow.
Some other object in the pipe. Hard to investigae but same principles as above - follow pipe back to last known good supply and check from there.
If the pipe goes over ground anywhere, check in case it has been buckled/restricted in some way?
Check for a supply valve outside the cistern (either another tap or a small fitting that has a screw adjustment on it) make sure that is fully open. If it's a screw fitting make sure the screw head lines up parallel to the pipe.
Just some ideas.
Drew, February 2009