By Karolin Schaps and Nina Chestney

LONDON (Reuters) - Britain's largest energy suppliers have been ordered to cap some of their most expensive tariffs by the country's competition authority after a two-year investigation that found providers have overcharged customers by billions of pounds.

Energy bills have doubled in Britain over the past decade to about 1,200 pounds ($1,640) a year, leading to allegations that utilities were overcharging customers.

Utilities have denied they have overcharged customers, but the Competition Markets Authority (CMA) found that British households overpaid 1.4 billion pounds a year between 2012 and 2015 because of uncompetitive standard energy tariffs to which about 70 percent of the largest companies' customers are subscribed.

"Competition is working well for some customers in this market, but nowhere near enough of them," said Roger Witcomb, chairman of the CMA's energy market investigation.

They will now have to allow rival suppliers to contact customers who have been on the most expensive tariffs for more than three years via a database that will be managed by regulator Ofgem.

The inquiry, which was launched in June 2014, concluded that Britain's "Big Six" suppliers -- SSE <SSE.L>, Iberdrola's <IBE.MC> Scottish Power, Centrica <CNA.L>, RWE npower <RWEG.DE>, E.ON <EONGn.DE> and EDF Energy <EDF.PA> -- will have to cap prices for customers on prepayment meters.

The CMA said the measure would save those customers about 300 million pounds a year in total.

"It is a tough set of measures, but we recognize where it will help drive the energy market forward to better deliver for customers," said SSE Chief Executive Alistair Phillips-Davies.

Shares in British-listed energy suppliers Centrica and SSE were down 9 percent and 10 percent respectively in early trading on Friday, in line with sharp losses across the wider equities market after Britons voted to leave the European Union.

Link to CMA report:

(Editing by Himani Sarkar and David Goodman)