Shouldn't be necessary to remove the handle from the spindle in order to replace the washer.
Is there a shield with a hexagon which you can unscrew?
Unscrew this and you will have access to another hexagon where the "bonnet" is screwed into the body. Need to isolate tap before doing this - i.e turn off any gate valve etc upstream of the tap.
When you have the bonnet/spindle assembly removed, then you could put it in vice to remove the handle if you want to, because it is probably seized and will require some loosening which would be best not done when it is still attached to the tap and a brittle ceramic wash hand basin.
JD
April 2009