Mr Cochrane likes to shock people by making predictions that sound nuts. Recently, he forecast that the next 25 years would give us three-dimensional videophones, machines that recognise body language and gestures, and e- mail that talks to you over a mobile phone, along with anthropomorphic robots, real-time language translation for voice and print, and even artificial skin.
What he wants most is a world of "three-click, one-second, no-handbook". In other words, he wants everything accessible within three clicks of a mouse, he wants it to appear in less than a second and he doesn't want to have to read up on how to do it.
Some of his wilder research projects have included studying ants: the notion was to observe how organic systems grow. He figures that by the early 21st century we will have supercomputers on our desktops - if we still have desktops - and by 2020 the computers will be wearing us.
"I don't worry about dying," he jokes, "but I worry about dying before my PC's proud of me." Many of his ideas sound similar to those propounded by Nicholas Negroponte of the Massachusetts Institute of Technology Media Lab; BT is the Media Lab's biggest sponsor. But there's a key difference: ask Mr Negroponte about the many rural kids, even in the US, who don't have computers and he says, "Wait 10 minutes." But Mr Cochrane knows immediately what you are talking about: he has been there.
Peter Cochrane grew up in a mining village in Nottinghamshire in a house with three books: a Bible, a dictionary and an atlas. In his village, he says, talented weekend musicians and artists spent their work weeks down a hole in the ground. Passing the 11-plus exam in that village made the difference between working in a shop (good) and working down the mines (not so good).
Mr Cochrane failed. He left his secondary modern school at 15 and got on a course at the local technical college trying to acquire enough skills to become an apprentice. He applied for his dream job, an assistant in a radio shop - he was a radio ham with a love of electronics and building radios - and was turned down. So he wound up at BT digging holes for cables and repairing telephones.
Having moved up the ranks to repair and install telephone exchanges and repeater stations, at 19 he started night school, where he had some private tuition in the subject that had held him back all along, mathematics - which made all the difference to his results.
"Suddenly I arrived with City & Guilds, HNC, and a couple of A-levels." At 22, earning pounds 1,000 a year at a time when pounds 600 bought you a car, he decided to take five years off to go to university. His wife, whom he married at 22, worked "night and day" to support them. Back at BT after finishing his degree, he was assigned to research on switching systems in Ipswich, had two children and finished an MSc and then a PhD, even teaching on the side. He runs an hour a day when his knees allow, and can nod off anywhere at any time but gets by on only four or five hours' sleep a night.
He is still a teacher, at University College, London, and at Essex University, and runs two master's programmes at BT. On top of all this, he branched into consulting work for a wide range of international companies: IBM, Hewlett-Packard, 3M, DuPont, British Aerospace. He ran a submarine programme to do seabed mapping; he worked for the UN in Turkey for six weeks, designing a transmission system. He is still doing this kind of thing: a month or two ago he was in Paris with Disney, working on a city for the year 2020 with Marvin Minsky of MIT, Disney's head of research and about 28 other people, just before spending a day or two with John Perry Barlow, self- styled "cognitive dissident" and Internet philosopher.
And Peter Cochrane writes: he counts 183 technical publications to date. He also personally remodelled his entire house: "My daughters know how to put in a ring main."
He has been head of research for about four and a half years, with an ever-increasing number of staff, even though during that time BT has slimmed down from 242,000 to 130,000 employees, with a further 15,000 to go this year. That the company's output and profits have gone up is, he says, due to the pounds 28bn investment programme that started in 1974 to change Britain's telecommunications infrastructure and is now winding down as BT starts considering the next programme.
One of Mr Cochrane's first moves was to ban paper in his organisation. He guarantees, though, to answer all electronic mail within 12 hours, 365 days a year. He does it, too.