To give away the ending, the letter arrives at its destination at 8am the next morning. Independent surveys show that Royal Mail is the most reliable postal service of any major economy, and also the most flexible. Even after next month's penny price rise, it will be cheaper in real terms than it was 10 years ago. The Post Office makes a profit too: last year pounds 472m on a turnover of pounds 6bn.
This efficiency is one side of a condundrum. The other is that on paper the Post Office, of which the Royal Mail is by far the biggest part, should be a template for inefficiency: a monolithic state-owned monopoly deeply steeped in tradition and with hardly harmonious industrial relations.
Last week postal workers voted two to one to give the Communication Workers Union authority to call industrial action over management's attempts to change working practices. The Royal Mail says it is trying modestly to update working practices; the union says it has lifted "half-baked dogma from American textbooks on Human Resource Management".
How can we reconcile the conundrum? When British Telecom and British Gas were publicly owned, they were rightly chastised for their incompetence. Can it be that Royal Mail has somehow broken the mould, and proved that a state-owned utility can be efficient? If so, why the threatened strike? And why is the management still so worried about Royal Mail's future?
At 5.30pm, the envelope is picked up from the post box by the familiar red van, put in a sack and driven through the rush hour to the Area Processing Centre - sorting office - at Nine Elms, south of the Thames at Vauxhall. This is the biggest sorting office in Britain, and one of the most modern. It employs 1,000 people and handles all the post coming from, or going to, south London: 1.1 million first-class items a day, 750,000 second class.
It is 6.15pm, and Nine Elms is starting to get busy. Some 75 per cent of all first-class post arrives in early to mid-evening. It must be out again by 9.45pm.
As Mr Pumpkin's letter is fed into the sorting system, one part of the riddle is solved. The level of automation is astonishing. First, the envelope is hurled into a drum which rejects those that are too thick. Then it disappears into the Japanese CFC (Culler Facer Canceller) machine. Here the envelope rushes through an S-shaped tunnel where an ultra-violet light seeks out the phosphor on the stamp. If it cannot find it, it flips the envelope round and looks again. Once the stamp has been dosed with UV light it glows and a sensor can tell whether it is first or second class. The envelope then whizzes though the "stamp cancellation module", and emerges the right way round (faced) and cancelled.
Nine Elms has had four CFC machines for five years. Each costs pounds 150,000, and allows 25,000 to 30,000 items to be sorted by six people in an hour. Close by are its predecessors, still used to sort the rejects. These need 14 people to face and cancel 10,000 items an hour.
It is starting to become clear why Royal Mail has been increasing its efficiency. A modest pounds 600,000 investment has tripled throughput and more than halved the manpower needed - a sixfold productivity increase.
But new machinery alone will not turn a bad company into a good one. There is no doubt that in 1974, when it logged the biggest ever corporate loss, the Post Office was a bad company; and that now - industrial relations apart - it is a shining example.
Tony Banting, manager of Nine Elms, and Alan Johnson, joint general secretary of the CWU, are on opposite sides of the dispute, but they agree on the key to the turnaround. Good managers took over the Post Office, and shook it hard. It probably helped that they believed they were working for their corporate lives - an internal document in the 1970s predicted the demise of the postal service in the face of electronic competition. But the achievements of Sir Ron Dearing, chairman from 1981 to 1987, and Bill Cockburn, managing director of Royal Mail from 1986 to 1992, then until last year chief executive of the Post Office (before joining the private sector with WH Smith) should not be underestimated.
Sir Ron was "a quiet, considerate man", Mr Johnson says, who brought his statistician's mind to analysing the problems of mail flow. It was he who queried Royal Mail's long-held belief that 90 per cent of first- class mail was getting through next day. He found the real figure was closer to 70 per cent - and ordered an overhaul of the way mail is transported.
Mr Banting says Mr Cockburn "brought vision and drive at a time when everything said we were going downhill". Though a Post Office man, he was by nature an entrepreneur, and managed to increase mail volumes by selling aggressively to the expanding direct mail industry. Couriers, who had almost annihilated the state parcel service in the US, were driven back both by Royal Mail and by the Post Office's Datapost service. "He was extremely imaginative," Mr Johnson says.
Mr Pumpkin's letter is taken, in a batch, to the next machine - the OCR/VCS or Optical Character Recognition/Video Coding System. This French-built machine is one of four that were installed three years ago at a cost of pounds 1.4m. First the machine's character recognition system tries to read the postcode and town.
If it succeeds it sprays pink lines along the bottom of the envelope; these act as as a barcode for the destination.
The letter from Clapham does not have a postcode, so the machine sprays a pink tag line higher up the envelope, and photographs the address. This image is sent electronically to a computer screen upstairs: an operator reads it, and types in the code for Aberdeen.
The OCR/VCS machines can read about half the addresses they see, and can process up to 40,000 envelopes an hour. When the sorting office is busy, the old slower sorters will be used - the giveaway is that they apply blue dots.
Had Mr Pumpkin's address been seriously deficient, the letter would have been checked by the "blind" sorters. They use computer databases to seek out the proper address. One envelope is labelled simply "Heny Thornton Centre". The computer cannot find it, but the postman knows where it is. "Often you've got it up here," he says, tapping his head.
The next machine sorts the envelopes into postal towns - it reads the pink codes and sends
them shooting into the right tray. Mr Pumpkin's letter is given another row of lines as the electronic code tapped in upstairs is married with the identifying tag, before it whizzes along to the tray for Aberdeen.
If all this seems state-of-the-art - some machines are only two years old - the Royal Mail has already decided it is obsolete. Next year all the existing equipment is being replaced by six Integrated Mail Processors. These 130ft-long giants, made by AEG in Germany, will cost pounds 2m each: total investment on IMPs will be pounds 200m.
One advantage is IMPs will be able to read 65 per cent of addresses. More important, they could help turn the electronic threat into an opportunity. Mr Banting says an IMP could for example read names and addresses off coupons, and send them electronically to their destination. The retailer, or whomsoever, would get its responses but would not have to handle any paper.
The company's frantic attempt to increase efficiency might seem unnecessary. It has, after all, seen off the couriers and is providing a good service to consumers.
But Royal Mail's managers remain convinced that the electronic Sword of Damocles hangs over them. They point out that post's share of total communication - inlcuding phone, fax and even advertising - has dropped from 20 per cent to 16 per cent since 1980; and they see e-mail as a serious threat.
It is this, Mr Banting says, that makes them so keen to change the relationship between themselves and their workforce. To those that say, if it ain't broke, don't fix it, he says: "Increasingly we are going to find it is broken." The current bit-by-bit approach to changing working practices will not, he says, allow the company to make the changes it needs in time.
There is a great deal of gunsmoke in the battle between Royal Mail and the CWU. Depending on who you believe, the unions are resisting widely accepted working practices. Or, the management has hamfistedly introduced trendy techniques that have managed to reduce rather than increase flexibility.
Much of the confusion arises from Royal Mail's strange mixture of advanced and antediluvian working practices. It has, for example, had only two grades since 1946, and every worker has been trained to do any job - sort, drive, deliver. Very flexible. On the other hand, it also has a military- style hierarchy (you do not come to work, you come on duty) and a rigid split between managers and postmen. Very inflexible.
Mr Johnson says the management's attempts at introducing Total Quality Management led to demarcation where there was none before. Managers counter that the unions are afraid that the new sytems will undermine their power. Whatever the rights and wrongs, something clearly needs to be done to break down the barriers.
Mr Pumpkin's letter is now bagged up with other post for northern Scotland. At 9pm it is taken by van to Stansted airport, where it is loaded on to a plane for the journey north.
This is part of Sir Ron's revolution. His studies showed that traditional mail trains were too inflexible for short journeys and too slow for very long ones. Now, mail travelling up to 100 miles goes by road. Between 100 and 200 miles, train is still preferred (a giant mail-only station is being built in north-west London). Beyond that, it could be a train or a plane: Skynet, which consists of 32 specially chartered flights, is the busiest night flying operation in Britain.
Arriving at the Aberdeen sorting office in the early hours of the morning, Mr Pumpkin's envelope is fed into a machine that reads the pink lines and classifies the letters by "walks". Bagged up again, the letter heads off to the sorting office at Inverpartick, where it is sorted finally by the local postman - he knows better than any machine how it should be delivered. At 7am he jumps in his van; an hour later, the letter is delivered.
In most respects the job of the delivery man is the same as ever. "The British post office, more than any other, is very conscious of being a public service," Mr Johnson says. Britain is the only country with two deliveries every weekday; in Australia, Sweden and Ireland there is no Saturday delivery while in North America you will not get post delivered to your door. In the UK, as fans of Postman Pat know, the mail will always get through.
And what of the argument over privatisation? It is irrelevant. What the Post Office needs is the freedom to compete fairly with its rivals. Whether it does this in or out of state ownership matters little - though it is essential that the Treasury be stopped from demanding apparently random dividends at will.
Like most things relating to the Post Office, the arguments are complex. But if they are resolved, there is no reason why Britain's most unlikely success story cannot run and run.