By Susanna Twidale

LONDON (Reuters) - Britain's energy regulator wants to trim 5 billion pounds from consumer bills over five years from 2021 by slashing the amount gas and electricity network firms can return to shareholders, it said on Wednesday.

Rising energy bills have drawn increasing public criticism, prompting Prime Minister Theresa May promise an end to what she has called "rip off" gas and electricity bills. The government has introduced legislation to parliament to cap prices..

Under its proposals, Ofgem plans to cut the "cost of equity range", or the amount network firms pay their shareholders, to 3 to 5 percent for the next regulatory period starting 2021, down from 6 to 7 percent now.

"In total, we estimate this would result in savings of over 5 billion pounds for household consumers, or about 15-25 pounds per year on the dual fuel household bill, who pay for the network through their energy bills," Ofgem said.

Under Ofgem’s framework, energy network operators set out their plans for investment and how much they expect this to cost over the period. Ofgem sets the return the companies can make.

Network firms said Ofgem's new plans could hurt investment.

"Ofgem will need to think very carefully about whether their proposals encourage the necessary investment in critical infrastructure that ensures resilience of the nation’s energy supplies," Scottish Power Energy Networks said in a statement.

Fixed returns have prompted investors to scoop up network assets in recent years, including Abu Dhabi Investment Authority, which in 2016 bought a 16.7 percent stake of the Scotia Gas Networks business from SSE (L:SSE) for 621 million pounds.

Other investors in Britain energy network include National Grid (L:NG), Iberdrola’s (MC:IBE) Scottish Power, Australian investment bank Macquarie and Hong Kong’s Cheung Kong Group.

Companies have until May 2 to respond to Ofgem's proposals with the final framework to be set in summer 2018. The current regulatory period runs from 2013 to 2021.

Ofgem senior partner for networks, Jonathan Brearley, told reporters the changes would affect company profits "but exactly how that plays into their margins is too early to say."

Brearley said the proposals offered attractive and stable returns but ensured the lowest possible prices for consumers.

Ofgem has been criticised by consumer groups for allowing the industry generous returns, while energy suppliers blame rising network costs for price rises. Ofgem data shows network costs make up about 26 percent of an average energy bill.

"We will be working through the proposals announced today, including Ofgem's opening view on what the cost of equity should be," said David Smith, the chief executive of industry body Energy Networks Association.

Ofgem also proposed cutting the regulatory period to five years from eight years, and proposed setting up an independent user and consumer group to challenge and monitor company plans.