If it's a 'ceramic disc' (which it sounds like). The only real repair route
is to change the innards. Turn the water off, hot and cold, remove the
innards using the big nut you can see. Pop down to your local plumbers
merchant with the innards AND one of the handles, they will need this to
match up the splines, you may need new handles aswell.. Hopefully they will
have a replacement set otherwise it is tap replacement time.