Is the spigot bearing no good ?, another way or removing is just to use a chisel and crush it in then pull out if you don't have the correct tool, the method with grease above works ok for most but never had much luck myself so just use me spigot puller.
Looking at the plate it appears the area you mention is recessed, so would be some kind of seal there, a bit of thin window draught excluder would work there, not seen anyway.
tabetha