Campaigners have welcomed news that the phone regulator Ofcom has warned four firms about generating "silent calls".
Silent calls: intimidating and annoying for many people
Carphone Warehouse was among the firms which made too many of the calls, which happen when dialling systems generate more calls than staff can handle.
Ofcom's rules ban silent calls and allow only 3% of calls to be accompanied by a recorded message.
The firms have until 6 December to respond, after which Ofcom could fine them from £5,000 to £50,000.
Carphone Warehouse also failed to provide recorded phone messages explaining to recipients why the calls had occurred, the regulator said.
David Stewart, from Ofcom, said: "We take the problem very seriously, we have the power to impose fines of up to £50,000 in relation to this kind of conduct.
"We're going to look at the question of whether to impose fines in the case of the four companies receiving notifications at this point, once we've received submissions from the companies."
Firms which broke the rules
IDT Direct Ltd, trading as Toucan
Brakenbay Kitchens Ltd
Space Kitchens Ltd
Following an investigation, the regulator found "reasonable grounds" for thinking Carphone Warehouse had breached the Communications Act 2003.
Its investigation found IDT Direct Ltd trading as Toucan, Brakenbay Kitchens Ltd and Space Kitchens Ltd were also in breach for the same reasons.
Silent calls occur when automated calling systems used by call centres for telemarketing, market research and debt collection generate more calls than the available call centre agents can manage.
When the person dialled answers the telephone, there is no agent available, resulting in silence on the line because the automated calling system has ended the call.
Many firms handle the problem by ensuring that a recorded message automatically plays when this situation arises but Ofcom rules decree that this system - known as "abandoned calls" - should not be used in more than 3% of all calls made in any 24-hour period.
Ofcom has since written to all four businesses informing them of its findings.
David Hickson, who has campaigned to stop silent calls, told BBC's Breakfast programme: "This is another small step forward, we've had lots of small steps over the last few years, let's wait and see what it really amounts to," he said.
"It's only when the industry see Ofcom actually act firmly against people that it will make any difference."
In a statement on Saturday, the regulator said it had found "reasonable grounds to believe that each of these four companies have engaged in persistent misuse of an electronic communications network or electronic communication services in a way that causes annoyance, inconvenience or anxiety to consumers".
Carphone Warehouse said it fully endorsed Ofcom's rules, and was working with the regulator "in tackling what is an issue across all industries that deploy automatic or predictive dialler marketing".
"We are and have been actively working both internally and with our third party agencies to ensure that, at the least, recorded messages are heard by the individual being dialled and that the proportion of abandoned calls falls below the threshold," it said in a statement.
The company also said it had already made "significant progress" in meeting the new rules relating to silent calls.