In a government-sanctioned report, Ofwat said that although reductions in customer bills are likely to be small, a more open market could ultimately end the "retail monopoly."
The regulator said: "It could lead to innovation, improved customer service, new offers - including bundling of products such as energy and telecoms with water - and, crucially, give customers the freedom to choose their supplier - ending the final retail monopoly."
At present, consumers have no choice over which water companies supply their households and Ofwat said that more competition would "prevent water customers being left behind in a retail revolution."
Cathryn Ross, chief executive of Ofwat, said: "The uncomfortable truth is that, when it comes to retail offers, water companies provide an analogue service in a digital age.
"Customers tell us they think they should have the freedom to choose and don't understand why water is the only retail market in which there isn't some form of competition."
However, the report added that there would be "significant costs" in opening up the market which would "ultimately fall on companies and customers."
Ofwat heard from a number of potential new entrants during its review which could see the opportunity from a new market to provide retail services more efficiently and to offer new products and services.
Ofwat added: "It is for the government to decide whether in principle it wants to introduce competition and, if so, how and when to do so."
Alex Neill, Which? director of policy and campaigns, said: "Giving people a choice over who supplies their water could lead to a better experience for consumers but any plan to open up the water market must learn the lessons of other utility markets.
"The government should now consider whether a competitive water market would deliver better outcomes for customers."
Labour's shadow environment secretary Rachael Maskell said that "water and sanitation is too important to turn into a market that doesn't work for consumers."
She added that "the solution for customers isn't to carve the water industry up further, bringing in more private suppliers."
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