E.on made the claims about charges for a heat network on its own website, www.eonenergy.com.
But watchdogs launched an investigation after two complaints that the claim "charges are designed to be no more expensive than heating provided by a traditional gas boiler" was misleading, and couldn't be substantiated.
The German owned energy provider said the claim was made on a "like-for-like" basis and included full maintenance and asset replacement provision.
The firm claimed that its heat tariffs were made up of an Energy Service Charge, which was a fixed price element, and the Heat unit rate charged as pence per kilowatt hour (p/kWh).
But the Advertising Standards Authority (ASA) upheld the complaints after finding E.on breached rules regarding misleading advertising, substantiation and other comparisons.
It banned the ad and ordered E.on not to include optional costs when comparing their service with traditional gas boilers.
An ASA spokesman said: "We concluded that, because the comparison included optional costs, which was not explained in the ad, the claim gave a misleading impression of the cost of District Heating compared with a traditional gas boiler."
He added: "The ad must not appear again in its current form.
"We told E.on UK plc not to include optional costs when comparing their service with traditional gas boilers, unless the basis for the comparison was clearly explained."