My kitchen tap won't turn on or off, it turns a little right and a little left but no cold water comes out the tap . Please help ?

Can you give a little more info?

Is it a single lever faucet? Does it have a hose coming out of main part of faucet?
Can you give us make and model?

Chuck

Yes it's a single 1. erm standard council tap fitting. Hot and cold single taps

I don't know what a council fitting is mmm and I do plumbing

Often on single lever faucets they get stiff inside and stop turning on and off all the way. Sometimes it just requires taking it apart and lubing inside with plumbers grease and all is well. In single lever many times the setscrew that is underneath the handle that hidden behind a very small pop out cap gets loose and the handle doesn't fully operate. Since we really not sure what you have I posted some vids that may help you out

Plumbers grease

http://reviews.homedepot.com/1999/20...ws/reviews.htm
.
Moen faucet
How-To: Repair Moen Single Handle Faucet, Pt.1 - YouTube

Delta
Delta Faucet Repair - YouTube

Amercain stabdard
How to repair a leaking kitchen faucet...Part 1 - YouTube

How to Fix a Leaky Kitchen Faucet Pfister Cartridge - YouTube
Price Pifster


Hope this helps

Get back need more info or maybe this will help you out