The report on the UK electricity market reform (EMR) said the savings could reach as much as £100 billion if gas prices continue to rise.
In terms of wind energy, the committee said the government should publish strategies for the further development of offshore wind, including setting out investment plans up until 2030.
Another recommendation was to introduce auctions for wind contracts and to pursue shorter contracts (15 years). Offshore wind investment should continue through to the 2020s, it added.
Committee chair Lord Deben said: "However, in order to secure maximum economic benefit for the UK, it is crucial that the government gives certainty to investors by legislating to chart a clear course well beyond 2020.
"Only then will we be able to insure against the risk of much higher future energy prices; enhance Britain's energy sovereignty; and protect ourselves against dangerous climate change."
In terms of offshore wind, the report represents something of a u-turn for the committee. In 2011 report into the development of a European supergrid, the committee described the UK's plans to develop 18GW of offshore wind by 2020 as "a big gamble".
At the time, it said that although encouraging and making use of the UK's huge offshore wind generation made sense, the report questioned its cost and reliability.