That message, which absorbs his every waking hour, is that the Post Office should be privatised.
It is a contentious point of view. The Labour Party and an awkward number of Tory shire MPs are against it, as are the industry's Union of Communication Workers and several consumer groups. Only last week, the National Consumer Council, which is funded by the Government, claimed that the public stood to lose from privatisation unless there were more safeguards on pricing and services. None of this cuts any ice with Cockburn, who combines the certainty of the true believer with the fervour of the evangelist. But then, he is chief executive of the Post Office.
'We have been advocating very strongly the business case,' he declared, 'which is that the world in which we operate is moving very fast, and if we are going to continue to be successful we need to have some of the public-sector restrictions removed so that we can compete in international communications markets. If you want a successful business, you have to remove the handcuffs.'
Cockburn, 51, a stocky, aggressive, Scottish Catholic, the eldest of eight children, is cranking up the propaganda machine to full pitch this month, because the shape of his remaining career is likely to be decided at this Thursday's Cabinet meeting.
That is one of the last formal occasions when John Major can press the green or red light for Post Office privatisation to be included or not in the Queen's Speech at the opening of Parliament on 16 November.
If Major waves it through, Cockburn hopes that the Bill to privatise the Post Office will receive Royal Assent by next July, paving the way for a stock market flotation by spring 1996.
That is a timetable tight enough for Cockburn to warn: 'If it isn't going to happen now, it will not happen this century, because of the timing of the next general election.'
If Tony Blair kisses hands as the next prime minister, privatisation will be expunged from the Whitehall vocabulary for at least the next five years, and even if the Conservatives pull off a fifth successive victory, the Post Office will probably not be at the top of their legislative programme.
The clock will be ticking loudly in Cockburn's ear by then. In February 2000 he turns 57, and retirement will be beckoning.
It is a measure of his frankness that he is willing to contemplate failure.
'If the decision goes against us, we will have to keep battling,' he said.
'Neither I nor my managers will throw the towel in. We would have to go banging on the doors of Whitehall, and we might become a confounded nuisance, but the future of the industry would require us to do that.'
That would set him off on yet another exhausting round of meetings with MPs and civil servants. As it is, two and a half years after the President of the Board of Trade, Michael Heseltine, raised the possibility of privatising the Post Office, Cockburn already feels he is coming to the end of what he refers to as 'a great Grand National' - not, hopefully, too much like the one with two false starts that had to be abandoned last year.
In a sense there was a false start in May, when Heseltine asked the Cabinet to sanction privatisation but was forced to settle for a Green Paper on the issue after pressure from Sir Teddy Taylor and fellow MPs who fear for their seats.
The Green Paper, which was published in the summer and asked for comments by the end of last month, made clear that the Government's preference is for the 20,000 Post Office branches to remain under public control, while 51 per cent of the shares in a combined Royal Mail / Parcelforce company would be floated on the stock market. The Queen's head would remain on stamps and vans, while prices and service levels would be protected by a regulator on the lines of those overseeing other utilities.
In an ideal world, Cockburn - who now earns pounds 236,000 a year - would like the Government to unload all the shares, to free the business from political interference. But he recognises that, in practice, Heseltine will have to be able to show that the state still has an important say in how the national postal service is run.
'It's clearly a political issue,' he admitted as he bounced around on the black leather sofa in his office north of the City. 'We've said to the Government that it's really their job to find a framework for us.'
The Post Office has been the framework for Cockburn's working life ever since he left school in Edinburgh at the age of 18 in 1961. He played soccer and followed Hibernian and, later, Glasgow Celtic. Nowadays, he said, 'I prefer international rugby. You get a tremendous atmosphere at Murrayfield and Twickenham.'
His exam results were good enough for him to qualify for university, but his father was a hospital porter in Edinburgh and with eight mouths to feed the family's need for money was paramount. However, Cockburn has made up for the lost opportunity through his children: his eldest daughter is now at Edinburgh University, and another is on the way there.
'My father and mother were very supportive, but life was always a challenge,' he recalled. 'Realistically I had to get a job.'
In those happy days when companies sought school-leavers rather than the other way round, Cockburn attended a careers exhibition and stopped by the Post Office stand. He joined as a trainee and two years later was managing a Glasgow telephone exchange.
But he saw more career opportunities in the postal side of the nationalised industry, so he got a job as an efficiency inspector, visiting post offices in East Anglia. Cockburn then gravitated to management services in London and became personal assistant to the late Sir William Ryland, the then chairman. Ironically, his successor in that job was Iain (now Sir Iain) Vallance, who switched over in the opposite direction, from post to telecommunications, and is now chairman of British Telecom.
'When I joined we were civil servants,' said Cockburn, 'and it was a seniority-based culture. You had to wait so many years before you could be considered for promotion. But now we have moved to a culture based on merit: that, rather than privatisation, was our burning goal during the 1980s.'
As part of that process, he had to take on Tom Jackson, the then leader of the UCW, whose handlebar moustache was a regular feature on 1970s television news bulletins. Bitterness still lingers from those battles. Mr Jackson has retired to Yorkshire to run a bookshop, but his wife said: 'I don't think he'll want to talk to you about Bill Cockburn.' He did not come to the phone.
The great watershed came in 1981, when Cockburn was promoted to the main board and BT was split off in preparation for its privatisation three years later. Meanwhile, Margaret Thatcher ruled out Post Office privatisation.
'That was frustrating,' Cockburn conceded, 'in the sense that we were surrounded by industries that were being freed. We could see early on that the same arguments held good for us as for these other industries, and it's taken us a long time to convince government that it's worth us having a go at it.'
Now, however, he admits he has his fingers crossed - just in case the Cabinet is tempted to duck the decision yet again.