Thank you very much indeed. I've tried exactly what you suggested and it works perfectly now - light in both rooms at last and dimmer works too. I have placed tape around the black lead where it entered the terminal so no bare wire sticking out now.
I've certainly learned my lesson though and...
My old dimmer switch broke so I bought a new one thinking I could easily change it myself. My big mistake was failing to take note of which wire went where and now I can get just one lamp working at a time. If you look at my photo you will see there are three wires, one black, one grey and one...