I had the same a couple of years ago. Cost me €90 at the time and a further €70 because the difference between the two meter readings wasn't taken into account. I have managed to get the €70 back after a long protracted series of visits to the water people. Fortunately, I always take electric and water meter readings at the end of each visit and record them on my PC organiser. Did you get a note of both readings on old and new meters ?
The thing is that you also need to "PURGE" the water meter when draining down and switching off. (There is another thread on here about it). If you look at the water meter, you will find on the inlet side a tap which drains off the contents of the meter after you have shut off your water supply. I now do mine, even if I am leaving in summer, just in case I don't get back. Have a look at the meter carefully and you should see the purge tap.
Have a look at the images on this post showing the purge tap location
Might be advantageous if Dave could make a sticky and post it on one of the forums, although the format of Pont Noir doesn't really lend itself to sticky's in as much as unless one makes a point of visiting specific forums, it may never be seen.
Maybe we need a sticky forum or maybe a forum entitled "Read this if you want to save yourself some money!" Guaranteed to focus the attention of visitors.