Wow what a mess - and good luck with Eon in the future - they are dreadful in my own experience.
Presumably you have a smart meter fitted which is why the readings on your bill started at zero (ie Eon know the actual real reading)
Firstly, why did you legally complete when you home wasn't finished 100%? It was of no benefit to you. In fact you would be paying a mortgage on a home you were not able to live in.
Did you get paid anything by the housebuilder to do this?
This should not be possible with CML certificates issued by the warranty provider confirming the home is 100% complete, and the mortgage loan can be released. My guess is you were arm-twisted to legally complete, even though you knew your home wasn't finished so the housebuilder (who are they by the way?) could have it for their year-end figures. Basically this could be regarded as mortgage fraud if you needed a mortgage.
Most site managers round up handover meter readings on the day by the near unit or two as it is a bit of goodwill.
He was trying to compensate you in advance for electricity and gas and water?) the site would be using, presumably in finishing your home. Unless a lot of overnight working was required and it was very cold in July the cost of utilities would be minimal.
To sum up, you are being charged for all the utility costs since the meter was fitted, including whatever cost the builder used. You should claim the difference from your housebuilder through the Small Claims Court if necessary.
Presumably you also took the meter readings when you did eventually move in?