Fault with kitchen tap not working, leak under sin

If the pipework is connected to the tap via push fit fittings try re-making the joint,preferably with a new fitting.

Your tap controls flow via a small ceramic ball with a hole through it. They are prone to cracking if residual water freezes. Although in theory your tap can be dismantled and the ball replaced, in reality the tap casing tends to resist unscrewing. Replacing the whole tap assembly is commonly required, but it’s quite easy if you have a long box spanner to use on the retaining nut underneath.