Ovo Energy has unveiled a 2.5% price cut in a Valentine's Day message to consumers urging them to "ditch the Big Six" and "feel loved again".
This comes as consumer watchdog Which? has urged regulators to refer the "broken" energy market for a full competition inquiry after figures showed that the Big Six energy giants received over 5.5 million complaints last year.
Ovo claimed that its price cut, its fourth since September, meant that its bills were £180 a year cheaper than the average of the Big Six which supply most UK homes.
The "insurgent" firm's chief executive Stephen Fitzpatrick told BBC Radio 4's Today Programme that many customers were paying more than they needed to for their energy.
"If British Gas charge the same for gas as the other five, their customers would save £900 million a year," he said.
"Their profits last year in the retail business were about £700 million. They have got 40% of the gas market and they charge about 11% more for gas than any of their peers.
"If you look at regional electricity suppliers, they all used to have a regional home base where they have much higher market shares than they do nationally. What we are seeing is that the incumbents from various different regions will tend to charge more in those regions, and that's where a lot of their profits come from - ex-incumbent advantage."
Ovo's call on consumers to "ditch the Big Six" comes after official figures showed the energy giants drew 5,579,665 complaints from customers over issues ranging from bills and metering to customer service, switching and payments.
Npower received 1,383,650 of the complaints received in 2013, the most of all six companies, closely followed by EDF at 1,240,005, British Gas with 1,235,550 and E.ON with 929,230. SSE and Scottish Power received 482,582 and 308,648 complaints respectively.
Which? executive director Richard Lloyd said: "Millions of people are unhappy with the service they receive from the suppliers which, combined with low levels of trust, is yet more evidence that more must be done to fix the broken energy market.
"Next month we want the regulators to refer the energy market to the Competition and Markets Authority and launch a full scale inquiry. This is the first and most important step towards a more radical reform of the energy market, giving hard-pressed consumers the confidence that they are paying a fair price."
Npower said: "We know we let many of our customers down following issues with our new billing system and, right now, our priority is to put these issues right.
"Since we issued a public apology to our customers at the end of last year, we have been reporting to Ofgem. We are making good progress and will soon be able to give an update on where we have got to. Looking at Which's proposals, there are many elements that we support and several that we are already doing."
A spokesman for Ofgem said: "The number of complaints is far too high and this reflects both poor company performance in 2013, especially from Npower, and low levels of trust. The onus is now on suppliers to use our reforms to re-build customer trust.
"Customer service is extremely important and Npower's performance is of deep concern to us. We have made it clear that Npower must improve its record on complaints and we have ordered them to report their progress to us regularly. Npower has accepted its failings, apologised to its customers and committed to making sure that no customer will be left out of pocket.
"We haven't ruled out further action on Npower complaints. We take supplier performance on complaint handling very seriously and in 2011 we fined British Gas and Npower £2.5 million and £2 million respectively for poor performance in this area."
He added: "We are already putting in place the most radical reforms to the energy retail market since competition began to make it simpler, clearer and fairer for consumers. As part of this, we have set suppliers enforceable standards of conduct so that they treat customers fairly. We therefore expect suppliers to raise their game on customer service, and if they don't, our reforms are making it easier for consumers to vote with their feet and switch."