Carphone Warehouse, along with Toucan and kitchen supply companies Brakenbay and Space Kitchens, continually breached the regulating authority's guidelines.
Their call centres used automated systems to dial residential numbers, but failed to connect the call to an agent.
Silent calls can feel menacing and cause distress to people who answer the phone.
Ofcom said the companies had failed to include a recorded message, as required, explaining the call had been abandoned. Companies must also ensure that no more than 3 per cent of calls made a day are abandoned, but Carphone Warehouse and other firms discarded up to 20 per cent a day.
A spokesman for Carphone Warehouse said: 'We fully endorse Ofcom's stipulations and are working with Ofcom in tacking what is an issue across all industries that deploy automatic or predictive dialer marketing.'
This year, the regulator introduced clear guidelines for companies and increased the maximum fine for abusing the system to£50,000.
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