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When I first visited the Greenwich Peninsula almost two years ago, I was, at best, agnostic about the Millennium Dome. The newly elected Labour government had given it the go-ahead not long before, and I was far from excited about the idea. I could not imagine myself wanting to go there when it was completed – if it ever was.

Then, from the river, I saw those dozen enormous umbrella-spokes – all that existed of the dome at the time – and I was hooked. Their scale exceeded anything I had expected. Being told that it would cover the area of two Wembley Stadiums or nine Royal Albert Halls had not prepared me for the vastness of the site and the boldness of the project. I saw the dome at the most dispiriting point in its construction, when it was covered in autumn mud, and it made me realise the scale and audacity of the reclamation of poisoned land in Greenwich.

I wondered whether the dome would meet its very tight deadline; after all, it had to be open and functioning in 25 months. But I saw immediately that, if it worked, it would be extraordinary.

I have visited the site three times since then. I have seen construction workers swarming all over the area and been briefed in an uncomfortable site hut before clambering around dressed in fluorescent jacket and hard hat. I was there just after the dome went up and I saw the internal fabric being installed.

A few days ago, I visited the dome in its semi-final stages. And I was staggered. Arriving by boat, a graceful pier led to the almost cosmetically tidy site. I saw the covered walkway – no need for anyone to get wet, even in the worst of weathers – leading from the Jubilee Line station (what a pity that London Underground obstinately refused to call it Dome Station) to the site. I was told that the dome area now had its own ecology, with birds, some rare, treating it as their new home.

Inside, some of the exhibition zones were in place. Acrobats were being hoisted up towards the vertiginously high roof, rehearsing for the big show on 31 December. Ancillary buildings, some of them enormous in their own right but dwarfed by the dome, had been completed.

The new McDonald’s, which was designed to blend into the total concept, was open and serving hamburgers. I was filled with admiration for the achievement.

A messy, polluted site has been transformed in a couple of years into one of the most attractive, indeed alluring, areas of our capital city

It is not just that a messy, polluted site has been transformed in a couple of years into one of the most attractive, indeed alluring, areas of our capital city. It is that this project, enormous in terms of both area and cost, has been brought in on time and to budget. Each time I visited the site, I wondered how all the elements – the dome itself, the infrastructure, the utilities, right down to the ticket machines – could be co-ordinated and invigilated.

I have immense respect for the architects, designers and building workers who pulled off this feat. But most of all, I admire those at the top of the project, who have managed to keep the big picture constantly in mind while ensuring that the tiniest details are not neglected.

I admire especially the woman in charge of the whole project, Jennie Page. Ms Page herself would not claim to be self-effacing. Indeed, I have told her that she makes Margaret Thatcher seem humble. But she knows what she is doing and she has almost – there are still a few weeks to go – succeeded in bringing about a perfect project – an international icon, visible from space.

She and her colleagues have not made this achievement seem easy or simple, however; it has obviously been very difficult and very complicated. All has not gone swimmingly. There have been misses, as well as hits, in working out the parking policies for a site that excludes private cars – a policy adopted in many parts of the world (the Getty Museum in Los Angeles, for example) but relatively novel in this country.

It could have all gone terribly wrong, or at any rate slipped from its schedule or exceeded its budget – as has happened with certain other lottery-funded projects. But it has not.