Ofgem said it had been assured by E.ON that all of the consumers affected had been identified and would be contacted and sent a rebate of an average of £14.83.
The amount includes 8% interest on the amount they were incorrectly charged.
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Rain will clear eastwards through Sunday but it will remain blustery.
Donald Trump has indicated he does not intend to block the release of thousands of secret files about the assassination of John F Kennedy.
Storm Brian will track off into the north sea later tonight. Blustery tomorrow.