What is the Dome but a great white elephant? It was the end of a hot day there, with the whole family in tow. I couldn't help fancying - perhaps I had a little sunstroke - that with a tweak of its white flanks and with Tony Cragg's sculpture adapted to become a trunk, the Dome could even be rearranged to look like an elephant.

But I have been keeping my thoughts to myself. Not one of my children would agree with me. They would be indignant. And they would not be alone. For the Dome - routinely written about as a flop - is attracting more than twice as many families as Alton Towers. And it is the children who most reliably seem to come out in favour of the experience.

The curious truth seems to be that the younger you are, the more likely you are to be impressed. My (almost) four-year-old twins, Bernie and Os, are in love with the place. They do not like to hear it referred to as 'the Dome'. They prefer to speak of it, with approving formality, as the 'Millennium Dome'. Millennium is not an easy word to get your tongue around when you are small - but the Dome has earned their tongue-twisting best efforts.

We arrived on one of the hottest days this summer - a party of six boys between the ages of 14 years and 18 months and assorted adults in an atmosphere of sweltering unreality. The building itself is suggestive of departure, somewhere between an airport and a spacecraft and there was, at the outset at least, a pleasant sense - enhanced by the weather - that we would presently fetch up on a more exotic planet.

But first we headed towards the Body - it was impossible to ignore its mighty, reclining form. We had to queue but a juggler was hard at work to keep our tedium at bay and none of the children minded waiting at all. I inspected the multi-coloured, tiled skin in close-up and thought the Body large and jaded. But the children were delighted by its size and by occasional sightings of a brilliant yellow trapeze artist swinging with casual grace beyond it. 'Look, you go in by the bum!' they exclaimed as we trooped inside.

Right from the beginning, the Dome staff could not have been nicer. I pushed Ted (18 months) up the body's escalators, through its bloody chambers and past its pendant, thunderous heart. Before each escalator, I was asked whether I was all right, and was the buggy safe on the escalators? The Body is not for those of a nervous disposition. Ted was not the only one who nearly jumped out of his skin when it started to make sounds as if overtaken by furious poltergeists. But the older boys were amused, especially by the room in which there were nine brains wobbling on sticks, one wearing a fez. I found the Body rather like a surreal department store, where nothing would induce you to shop. But once inside, we were carried along, as if part of its bloodstream.

I preferred the section called 'Mind' and marvelled at Ron Mueck's boy in his larger-than-life reverie. I was sorry to learn (from another forthcoming member of staff) that Helen Chadwick's 'brain' has been removed because someone had stuck chewing gum on it and Chadwick's estate had con cluded that the security at the Dome was inadequate.

'Talk', my stepson Tom (14) pointed out, 'seemed like an ad for BT'. It did not take long to discover just how right he was. (It is sponsored by BT). However, Tom and his brother Theo (12) relished the interactive 'Avatar' where you can be changed into a cartoon character. This is how Tom described his experience:

'I went into a small booth twice the size of a BR toilet. An assistant made me tuck my shirt in and stand in a certain way with my feet apart and my arms at 45 degrees to my body. They took a photo of me three times in different positions. The assistant superimposed various dots over the picture of my face. I got two pieces of paper with details of how to access my avatar. I then went to a screen where a 'virtual me' pranced about on a flying bike around the dome with ET.'

The Dome is full of stray actors, as if they had been released from a play and had subsequently got lost. People in Tudor costumes stroll about like lost souls, a robot lets off steam, a couple of jugglers perform, seemingly to please themselves. Of these actors, the ones we liked best were three frumpy women in macs and headscarves with elongated noses like monster parsnips. They walk around arm in arm and stick their noses into everything. 'They're really men,' said Leo.

Bernie was in a state of high excitement in an area called the Time Keepers. I could not work out what this area had to do with time. It was a chaos of plastic balls, fired from balconies. It was like being inside one of Professor Brainstorm's inventions - and extremely noisy. The Dome is in love with noise. After trekking around for hours, it was a relief to stop off in 'Rest'. And while after a mere five minutes, I had had my fill of the music that is supposed to go on for a thousand years, I appreciated the cool of this pink catacomb and was diverted by the prostrate visitors reclining on their plaster beach like misdirected sunbathers.

We saved the 'Millennium Show' for last (there are two shows a day and it is a good tip to see the afternoon show because you can then go to popular places in the morning without queueing and even achieve a quiet, uncrowded lunch at McDonald's or Aroma).

By the time we sat down in the vast auditorium, we were wilting with weariness and even ice cream could not be guaranteed to keep temperament at bay. But it was bliss to be still and cool inside the theatre space and suddenly it occurred to me: the circus is what this building is for. It is a permanent Big Top - so big that the brave couple who unravel themselves at the top seem almost lost in the space; the eye could easily abandon them for ever.

The show was the high spot (in every sense). And I was amazed and delighted by the relaxed atmosphere in which one can, if one chooses - and we did - park oneself in a café to watch the show, or sit on the floor crosslegged, near the stage. My partner said, at the end of the day - which happened to be Father's Day - that it was the best he could remember. Tom said that while he couldn't put his finger on what he had enjoyed most, he was sorry to leave. But the Dome is clearly for the newest of the new generation: Ted was in heaven. He shouted and pointed at the miracle of the flying people. He swayed in time to the music and then suddenly, as if finally making up his mind about something, he took off across the floor, crawling with great speed and laughing - in the direction of the stage.

Tour guide

Getting there: Go by Tube on the Jubilee Line: the Dome station is North Greenwich.

Entry: The queues were short, smooth and well managed. Family £57 (two adults & three children or one adult & four children). Adult £20; senior citizen £18; child (five-15 and student card holders) £16.50; children under five free. ES40 card holders £12. 'Taster Tickets', at £10 per person, are available at the gate after 4pm.

Ambience: Calm, spacious but with lots of noise in certain areas. We were all a bit baffled at first by the scale of the place and not sure what to do. You need to allow a day to get your money's worth.

Food and drink: Several familiar High Street chains. The kids were content with McDonald's. We managed to find good prawn sandwiches at Aroma. Could have been more imaginative but works fine with children.

Navigation: The signposting is OK once you get the hang of it.

Kid's favourite feature: (varied: see right).

Parents' favourite feature: Ron Mueck's 'Boy' was my favourite attraction - a magical sight.

Most disappointing feature: The 'Journey Zone' was nothing like as exciting as it could have been.

Our tip: Go to the afternoon performance of the Millennium show. Most people choose the morning one, leaving the other zones wonderfully empty.

Kids' verdict: A great day out.

Parents' verdict: An agreeable day but a missed opportunity. Maybe the Japanese will do better.