I have a mixer tap in the kitchen. The hot tap works fine, however the cold tap has a burst of pressure then falls off after a second, If you keep turning the tap further and further on the water comes out at a high pressure.

Is the problem with the washer or is it another part of the cold tap?

I'm assuming that your faucet is a two knob valve and noit a one handled one. Turn the water off to the valve and remove the cold water stem and washer assembly. Check the seat for any trash caught up down there. Now turn the cold water back on the flush out the supply. You should have a strong stream when you do this. Reassemble and test. Better now? Regards, Tom