The gas regulator Ofgem should "focus on getting the best deal for customers" by setting companies more "challenging efficiency targets", MPs have said.
An extra £820m could be cut from bills, MPs say
The National Grid sold half of its eight regional distribution networks in 2005 for £5.8bn.
The Commons public accounts committee found these deals were likely to mean savings of £325m by 2023 - or customers paying £1 a year less for gas.
But there was potential for £820m more in price reductions, the MPs said.
The committee, which heard from Ofgem representatives, said the distribution network deals had been struck "on the basis that they did not result in a net detriment to consumers, rather than because they would bring benefits to consumers".
Its chairman, Conservative MP Edward Leigh, said this was "far too cautious a stance".
He added: "As gas prices go through the roof, Ofgem must do everything it can to get the best possible deal for gas consumers.
"Certainly, they cannot wait until after 2013 to enjoy most of the benefits of the sales of the networks, as Ofgem currently expects."
Mr Leigh said Ofgem had to be "bold" in setting price controls when the next review happens in 2008 and called for efficiency savings of at least 3% a year.
He added: "And the regulator must make sure that the regulations it imposes on the gas industry genuinely encourage innovative and efficient behaviour and that lower gas distribution costs really do result in lower gas bills."
Earlier this week, the Conservatives called on the Office of Fair Trading to investigate whether gas customers are being ripped off by high gas prices.
Party leader David Cameron said he wanted people to "live for less...starting with utility bills".
The average annual gas bill was £630 in October, up £300 from 2003.
Meanwhile, British Gas customers who do not pay bills within 28 days are to be fined £5 from March.
Ofgem has advised households to switch suppliers to avoid the penalty.
But Duncan Sedgwick, chief executive of the Energy Retail Association, said: "What we have here in the UK is the most independent, liberalised and transparent market anywhere in the world.
"An inquiry of this kind would achieve nothing whatsoever."