Tall lamp - partial repair (Crookes (S10))

I inherited a tall standing lamp with a main light at the top and a reading light halfway down.
The main/top light has stopped working (no, it's not just the bulb!), but the reading light still works fine.
I don't know how to fix it but I suspect the switch for the top light (in the centre of the unit, see pictures) needs repair. If you can fix it and would like it, it's yours! (Or if you just want it for the reading light too)