Ahh right, no worries.
As long as they arent all going into one RCB (circuit breaker)!
p.s. weird to have an RCD in a house. Maybe its standard now, I cant keep up with all the building regs, but when I was studying, an RCD was to stop people from getting electrocuted and thats its only use.
Anyways... back to the soldering iron. I'd look for a fault with the iron itself.
Can you plug in your kettle to the same socket as the iron is tripping out on? Turn the kettle on - this is a fairly high drain and if it doesnt trip out, then its the iron.