Millions of customers could save up to a £1bn a year on the cost of their landline, broadband, TV and mobile packages under new Ofcom rules forcing companies to offer the best deals when their contracts come to an end.

The broadcasting and media regulator’s new rules, which come into force from Saturday, could benefit the estimated 20 million customers who are paying over the odds because they are out of contract and not aware of better deals.

Phone, broadband and pay-TV companies will be forced to tell customers when their contract is coming to an end, what they are currently paying and what the best deals are on offer.

“Millions of people are out of contract right now and paying more than they need to,” said Lindsey Fussell, consumer group director at Ofcom. “These new rules make it easier to grab a better deal.”

Ofcom has found that the biggest savings relate to broadband deals, with 25,000 customers a day coming to the end of their contract, which usually leads to an automatic price rise. There are about 8.8 million broadband customers out of contract, which the regulator estimates could be saving about £100 a year through better deals with their existing provider that they are currently not made aware of. Ofcom said in the case of some customers, savings could be £150 annually, depending on their provider.

About 1.4 million mobile customers could save an average of £75 a year, and some up to £150, by moving to a better package at the end of their existing deal.

The regulator found people who bundle their landline and broadband services together pay, on average, about 20% more when they are out of contract and have not shopped around. This rises to 26% among customers who bundle their pay TV with these two services.

Under the new rules, telecoms and pay-TV companies will be forced to warn customers between 10 and 40 days before their contract comes to an end. In addition, they must state what a customer has been paying until now, the price when the contract expires and the best deals available, including any prices only available to new customers. These alerts will be sent by text, email or letter, similar to other sectors such as insurance and energy providers.

The introduction of the rules to the telecommunications market follows a similar crackdown in the home and car insurance markets.