Why has my bathroom cold water tap (but no others) stopped working?
We just had this happen - there was an airlock in the cold water pipe to that tap. As the tab was a mixer (two knobs, one spout), a simple solution is to put your thumb over the end of the spout, open the cold water completely (nothing happens) and then turn the hot water on. Blocking the spout means the hot water is routed back up the cold pipe, eliminating the air lock.

Use a cloth/rag if your hot water is too hot to keep your thumb over the end - it takes a minute or two.