I read this when I was in primary school, which means it was written before the very early 1980s. I suspect it was written by a Brit.
England is experiencing a long, hot, dry summer; it's hot enough that dragons start hatching out, and terrorizing the country.
A couple of kids decide to head off and figure out how to stop the plague of dragons - I can't remember if they intend to find him, but they ultimately find St George, and he checks his weather machine. There's a dial on the machine that's stuck, so England's been getting no rain, which means that the weather is dry enough that the dragons can hatch. They re-set this, and everything gets cleared up - I think the dragons all die off when it starts raining again.
There's one other scene that I can recall, that I'm not entirely sure is from the same book. Our questing children are up in the sky somehow, and stumble across the department that's responsible for making rainbows - there's a workcrew busy painting up rainbows to display in the sky the next time it's raining.