Hi, my bathroom tap has recently decided not to give out any more cold water, I can turn it on full and there is nothing,this is a hot and cold tap coming out of the same spout , could it be the washer? If so how do I replace?

Minerals that have built up on the pipe walls have broke loose and now are clogging the inlet ports on the cartridge in your faucet. The solution would be to shut the water off and open up the faucet. Check and clear the inlet ports in the cartridge. Before you button up, place a pan over the open valve body and turn the water back on for a minute to flush out the supplies and valve body. Reassemble and test. Good luck, Tom