Andrew MacKinlay, Labour MP for Thurrock, said he will be writing to Michael Heseltine, President of the Board of Trade, about the thousands of people who had been "enticed" by the offer into purchasing Mercury One-2-One telephones. Many customers had been "thwarted in their efforts due to excessive demand and inadequate planning and facilities", he said.
Mercury should, at the very least, offer dissatisfied customers free calls by way of compensation, he added.
A Mercury spokesman said the offer was made to people who joined after 8 November that they could make an unlimited number of calls.
But he said: "We experienced 10 times the average number of calls made on a Sunday."
He said Mercury had not anticipated such huge demand.
"We are dealing with the complaints case by case and we will recompense those who were unable to use their phone."
Mobile phones were among the most popular gifts this Christmas, with some 750,000 people joining up to the four major networks.
The Mercury spokesman added that at least 20 people had spent more than 12 hours on the phone on Christmas Day, and another 20 had made more than 2,000 calls between them.
"It may well be that the amount of time these people used the lines prevented others from doing so," he said.
But a £75 compensation offer for a Mercury mobile phone customer who tried and failed to make free Christmas calls was labelled a "joke" yesterday.
Sally Pope, 27, a sales manager from Camden, north London, bought her One-2-One Mercury mobile phone because of the company's offer of free calls worldwide on Christmas day.
She had drawn up a list of friends and family members to call all over the world to make the most of the Mercury offer, but spent a day trying without success to get a connection.
She said: "I feel cheated. My Christmas has been completely ruined. I spent all day on that phone thinking I was bound to get through in an minute.
"I complained and they made me an initial offer of £40. I told them it was totally unacceptable.
"Then they came back to me and said they were prepared to make a final offer of four months' free line rental, which adds up to £50, plus another £25.
"The compensation offer is a joke. I'm really angry.
"When I tried to get through to customer services, they were closed. It's a complete shambles.
"They've said I can just get my money back on the phone but that doesn't compensate me for the hassle I've had."Reuse content