Sorry, bit late on this one!
However, for any one else faced with a Protector lamp base that won't undo, Mr.C's top tip! :)
Stand the lamp in boiling water out of the kettle, to about 1/4" below the joint line between the base & the upper part of the lamp.
(If you have a diagram of the lamp, it's the joint between the vessel & the glass plate).
Leave for a couple of minutes, remove from water and unscrew while still hot (but wrap the base in a cloth first to save burnt hand!)
Done lots this way & so far it's worked on every one. Even those cemented up with years of Brasso.
We inhabit an island made of coal, surrounded by a sea full of fish. How can we go wrong.......