The company, which has been overwhelmed by inquiries about One-2-One, has written to anyone who subscribed in the first two weeks saying that no connection charge would be included in their first bills.
In theory, customers can register for One-2-One within minutes by telephoning a customer service number. But, having bought the telephones, some people were failing to get a reply from the number or found that registration was taking up to 72 hours or more.
A spokesman for Mercury One-2-One said: 'It was a human congestion problem which led to huge delays.'
Mercury declined to say how many people have registered for One-2-One, which is initially available in Greater London and surrounding areas. The figure is thought to be between 8,000 and 10,000, of which two- thirds are completely new to mobile telephones. Mercury said that the number of people employed in customer service has been trebled.