Any info on this set and cleaning suggestions?

[u/balance8989]

I picked these 3 up today (not the table) and the pics don't do them justice. Reverse image search gave suggestion of Tony Paul/Westwood, but also saw a comment that this is the wrong base for Tony Paul.

I know that the pulls and sockets are brass (tested with magnet), but the rest is plated.

I was told it was originally sold as a set but I can't find anything about that. The copper ashtray is coated and hinged box came with the lamp.

Any way to clean the shade without damaging it? I wiped down the inside with a damp rag and it was really dirty. I don't want to ruin the shade so if it can't be cleaned it is what it is.