Lord Davies of Oldham said the widespread use of hand-held mobile phones while driving was a danger to the public because motorists were distracted from traffic.
Peers gave a formal first reading to his Road Traffic (Use of Mobile Telephones) Bill, but it has little chance of becoming law because of lack of Government support.
A spokesman for the Department of Transport said present legislation was sufficient because the police could charge motorists for driving without care and attention.
The Government also ran a joint campaign with mobile phone network providers to discourage drivers from using their phones last year.
Earlier Trade and Industry Secretary Stephen Byers announced his decision to auction five third-generation licences, paving the way for at least one new network operator. Third generation mobile phones will enable users to surf the Internet, exchange e-mails and hold video-conferences on the move.