I have an answer that might be useful to some people experiencing very poor fuel economy with a Honda Jazz.
Our Honda Jazz was first registered in July 2004. We bought it second-hand five years ago.
This year the fuel economy started dropping from its original 5.7L/100km to a disastrous average of 7.0 this month (August 2019).
We live in a Mediterranean climate, which is typically hot and dusty all summer, with very little rain, so this was not a cold running problem. Initially, I attributed the heavy consumption to my wife's poor driving (she has no idea what gear she's in most of the time). I also thought that the airconditioning system might be affecting consumption (but not as much as this!) I did check tyre pressures.
However, I noticed a distinct lack of power at low RPM on familiar, steep, uphill stretches to the point where I was definitely having to use a lower gear than previously. Switching off the aircon made no difference.
Initially, my bet was on a faulty oxygen sensor or lack of power to its heater. I'm glad I didn't put money on that because my mechanic traced the problem to a BUILD UP OF DIRT INSIDE THE THROTTLE CHAMBER. He removed this, cleaned it thoroughly, and the average consumption is now down to 5.2 litres per 100km! (I think that's well over 50mpg.) Update: today the average is 5.5 with shorter journeys and I expect it will rise to the original 5.7 over the next week of "typical" driving. (It's very mountainous here.)
I believe that this dismantling and cleaning is a fairly easy DIY job so it's worth doing if you, too, drive in a dusty climate or through, say, a dusty car park each day.
My mechanic said that a faulty ignition coil can also cause poor fuel economy, but that wasn't the problem this time. (The engine has two spark plugs per cylinder. If one isn't working, it's not obvious but it will affect performance.) He also said that on high-mileage engines, the exhaust & inlet valves can cause poor fuel consumption. (They are adjusted automatically, hydraulically. In cold weather, you'll often hear one or two tapping until the engine warms up. If the tapping continues when hot, you've got a problem.)
I note, too, that others say the AGR valve might need to be cleaned.
I hope this info. helps someone else!