Whenever I fit a new washer I always, always strip the tap head apart , clean it and lubricate it. I then reface the tap every time, even if I only skim the tap face slightly. Doing this as TB says is a standard procedure every time. If you have gone as far as taking the tap apart there is no point in doing half a job, you might as well service the whole tap given the opportunity. It will then operate much easier with a smear of petroleum jelly on every threaded surface.
15 years ago I did nothing but service taps all day long, every day, at that time it was normal to have British standard taps in almost every house.
Today people wont pay for British taps and buy the trash imports brought in from abroad. So we all end up with these cheap taps that are not suitable for re-surfacing or repairing. You just buy new ones and chuck the old ones.
Going back to your problem .. if the washer was a push fit, whereas it gets pushed over a short spindle with a nipple on it. The chances are that the washer may have ridden up over the spindle slightly and need re-fitting.
Remove the washer and smear some vaseline in the hole before pressing it back onto the spindle and force the edges down with a flat edge.