Why, then, has he not joined the ranks of hero businessmen, alongside Richard Branson and the like? Perhaps it is because he is respected rather than loved, admired rather than liked. Perhaps it is simply because he is beastly.
The vocabulary evoked by the Channel tunnel supremo rarely varies. He is a bruiser, a battler, a fighter. He is fiery, acerbic, abrupt and - one of the favourite media epithets - abrasive.
He is described thus because it happens, by and large, to be true. All his enemies, and he has plenty of them, say so. But so do his supporters. Take this assessment from a friend of long standing: 'Alastair is immensely able, and he has immense drive. He is probably the only man who could have got the project to where it is now. But he also has an extreme and unnecessary weakness in always attacking people. In almost any company he starts the conversation with a blow to the face. His abilities would be put to better use if he did not feel the need to fight everybody all the time.'
Nobody appreciates that better than the 10 contractors in Transmanche Link who have built the tunnel for Sir Alastair. The six-and-a-half-year construction phase was scarred by some of the ugliest and most public corporate spats Britain has witnessed. As costs escalated - the project has come out at double the original estimate of pounds 5bn - and timescales began to slip, Sir Alastair and TML fought like rats in a sack. Sir Alastair did not bother with diplomatic language. He talked about 'blackmailers' and said he had 'a severe inability to tolerate deceit'.
Although the contractors remain the principal targets for Sir Alastair's spleen, he is not fussy about roughing up anyone else who sees things differently - be they bankers, brokers, journalists, public railway operators or even governments.
A construction analyst with a firm of City brokers tells the story of how he and his wife were introduced socially to Sir Alastair at an art exhibition, only to be treated to an unsolicited and offensive tirade against the chairman of one of the five British contractors in TML.
In the early days of the project, when its survival was far from certain, sceptical journalists would be hauled off to Eurotunnel's merchant bankers to be given the verbal third degree by Sir Alastair.
And then, of course, there are the acidic letters and faxes, fired off at the drop of a hat. Anyone who has had dealings with Sir Alastair will have a drawerful. And while it is not comfortable to be his enemy, it is no picnic to be his ally either. As one insider says: 'He is harshest with those he trusts most. In fact he can be frighteningly belligerent.'
Quite where these pugilistic tendencies come from is as much a puzzle to friends as enemies. Another friend says: 'In private life he can be witty and charming. With Alastair it really is Jekyll and Hyde.'
It has been suggested that Sir Alastair, South African by birth, is aggressive because that is the only way for an outsider to make his mark on the British business establishment, though one can think of plenty to whom that does not apply.
He was born in Johannesburg in 1938, the son of a Scottish oil executive who had married into one of the country's oldest Afrikaner dynasties. His mother's family dated back to the early settlers of the 1650s. His parents divorced while he was still young and his mother went on to remarry twice. If this caused disruption, it was not reflected in the young Morton's academic achievements. He went to Witwatersrand University two years early at the age of 16 to study classics and mathematics and then won a De Beers scholarship to Oxford.
He joined De Beers at 21 and was sent first to Rhodesia, just as majority rule was being phased in, and then back to South Africa. Despite his ancestry, he was no friend of apartheid and he stomached it for only three months before moving to the United States, where he married Sara Stephens, an Englishwoman he met in Rhodesia, and worked for the World Bank.
He arrived in Britain in the mid-Sixties and made his mark almost immediately by joining the Industrial Reorganisation Corporation - the vehicle for Labour's interventionist economic strategy that came to be known as Harold Wilson's merchant bank.
Morton left the IRC in 1970 and spent the next six years doing the rounds as a company doctor, rescuing stricken engineering concerns, before returning to the state sector as managing director of the British National Oil Corporation.
It was there that he had the first of the spectacular bust-ups that have punctuated his business career, clashing with the chairman, Sir Philip Shelbourne, over the privatisation of BNOC. Morton was forced to resign and spent two years in the wilderness until the Bank of England prevailed upon him to rescue the ailing banking group, Guinness Peat.
He set about the task with vigour, selling off its corporate assets in the face of opposition from the bank's founder and main shareholder, Lord Kissin, with whom Morton publicly rowed. Guinness Peat subsequently surrendered to a hostile takeover bid from the New Zealand holding company, Equiticorp, and Morton resigned to take on the ultimate challenge of the Channel tunnel.
Sir Alastair may be loathed by those with whom he has crossed swords in business, but he is without pretension or side and is a refreshing antidote to the grey men in grey suits who inhabit so much of British commercial life. He lives comfortably in St John's Wood, north London, in considerably greater matrimonial harmony than his parents.
Now that he has got his train set to play with, surely Sir Alastair will calm down. Sadly, the answer is almost certainly not. He thrives on crisis management, on conflict. The prospect of running a stable business bores him. 'It is a restless compulsion to keep stirring things up,' says one associate. 'Alastair will not let things settle. He prefers hyperactivity to calm. He worries if things are quiet. As a result, he finds it difficult to delegate and that is why he has surrounded himself over time with people he has been forced to trust.'
Sir Alastair's 56th birthday falls on Tuesday. It coincides with the long- awaited announcement from Eurotunnel of the fares it will charge when its car passenger service starts in May. Although this will be a crunch moment in the commercial life of Eurotunnel, Sir Alastair will not be there. He has also announced his intention of giving up the post of chief executive this July, once the tunnel is up and running.
The consensus among friends and foes is that without Sir Alastair, the tunnel would never have got this far. Had he not been parachuted in by the Bank of England to salvage the project in 1987, the tunnel would almost certainly have stayed on the shelf for another generation. Whether it has been worth all the grief is another matter.
Sir Alastair says the battles that have raged around the tunnel have largely been about money, not personalities. In a narrow sense that is true, since pounds 10bn buys a lot of arguments.
But that does not explain why so many of the contractors found Sir Alastair intolerable to work with, none more so than Jack Lemley, a hard-bitten American drafted in as chief executive of TML half-way through the contract. Their antipathy is legendary. Lemley was utterly uncompromising, a brick wall. 'I do sometimes wonder whether Alastair saw his mirror image in Jack,' says one insider. 'They are both Capricorns, you know.'
Nor does lucre alone explain why Sir Alastair discarded so many of his own senior executives in such short order. Take Tony Ridley, who was brought in from London Underground to manage the construction side of the contract for Eurotunnel, only to be sacrificed a year later following yet another run-in between Sir Alastair and the contractors.
There is also a view, prevalent among the contractors, that Sir Alastair's temperament has cost his bankers and shareholders money. As the chairman of one of the TML contractors says: 'Morton has done a good job, but a less combustible and egocentric style might have achieved the same result more cheaply and more quickly.'
Quite what he will do next is anybody's guess. Two months ago the Chancellor, Kenneth Clarke, gave him the task of spearheading the Government's initiative to get more private finance into public projects.
Apart from appealing to Sir Alastair's interventionist instincts, the appointment was a masterstroke in other respects. Not only did it silence one of the Government's most vocal critics on the subject, it ensured the Treasury a taste of Sir Alastair's rottweiler management techniques, with minimal political comeback for Mr Clarke.
Whether a project that is 100 per cent over budget and a year late is necessarily a good advertisement for a government initiative is a question that, unusually, reduces Sir Alastair to prevarication and defensiveness. Hardly his normal style. Perhaps he is starting to go soft after all.