The E.on customer service number is currently:

0845 303 3040

E.on now have an 0345 number that customers can call in on for billing enquiries, payments and meter readings.

0345 052 0000

I'm told this number will cost the same as an 01 or 02 number, same as a standard line number. This should be the same for both mobile and landline phones, check with your provider though.
03 numbers have been assigned by OFCOM to replace numbers beginning with 084 and 087.

E.on's website page with all their numbers can be found here https://www.eonenergy.com/for-your-home/help-and-support/Telephone-numbers

Please do not leave messages for E.on here, I am not E.on, I don't work for E.on, I have just provided the information for you.