In a press release at the time, Racal heralded its "exciting" plans to create a "truly portable and mobile nationwide public telephone network unavailable today".
The statement suggested the service would find favour "among people constantly on the move such as business executives, sales representatives, journalists, doctors and veterinary surgeons" as well as vehicle fleet operators.
Its authors can little have known then how the clunky, cumbersome technology would change over the years into lightweight, universal devices - or how etiquette about their use, for example by motorists, would develop.
The press release boasts how a subscriber "travelling by car between London and Edinburgh or Exeter, for instance, will be able to make or receive national and international calls with ease throughout the entire journey".
Vodafone's name was a conflation of the words "voice", "data" and "phone".
It was conceived by one of the company's original directors and the advertising agency Saatchi & Saatchi - which had earlier been behind the 1979 Conservative election advertisement with the slogan "Labour isn't working".
Then chief executive Sir Gerry Whent initially rejected the agency's proposal to spell the name with an "f" instead of "ph".
But he later relented, reputedly saying "in for a penny, in for a pound - you can have your flipping 'f' as well".
Vodafone says it is now the UK's most valuable brand and the 16th most valuable in the world.
It became the first mobile network to launch in the UK with a call made from St Katherine's Dock in London on January 1 1985 to Newbury, Berkshire - home of the company's headquarters.
The firm was demerged from Racal in 1991 and was floated as an independent company in London and New York. In January 1999, Vodafone connected its five millionth UK customer. Racal was later swallowed up by France's Thales.
Vodafone today describes itself as one of the world's leading mobile communications providers, with almost 360 million customers including about 19 million in the UK, where it employs more than 8,000 people.
It operates in more than 30 countries and in partnership with networks in more than 40 more, and has a market value of about £60 billion.
Vodafone last month completed one of the biggest transactions in corporate history when it sold its stake in American joint venture Verizon Wireless for 130 billion US dollars (£78 billion).
It saw the group share out around £50 billion in stocks and cash to shareholders.