Any ideas why my cold water mixer tap won't work?

Well. it's one of three types: rotary-ball, ceramic disk or a 'cartridge' .
The actual faucet handle is removed with a hex wrench or a screwdriver, depending on what you've got there.
When you get it out, look for corrosion or foreign goo in the cold side of the disk/ball/cartridge.
Best to head over to your local hardware with it and they'll
know what's what with it

Jim
September 2006