No matter how fancy your light fixtures are, in the 18th century, they're still powered by good old wax-and-flame candles just waiting to set your house on fire…unless it's magically fueled by experience.

Henry states,

I have but one lamp by which my feet are guided, and that is the lamp of experience. (13)

To put it another way: leopards don't change their spots, and you can't teach an old dog new tricks.

That means he expects Great Britain to continue to behave in the way they've been behaving for the past ten years, so he's ready to turn out the lights on that relationship. Or to put it in Henry's historical context, blow out the candles.