IN New York they salute astronauts and presidents with tickertape and marching bands.

In London yesterday at the Olympics victory parade, they said it with comfy shoes, tuna sarnies, and restrained but heartfelt cries of: "Well done everybody, well done."

It was a peculiarly British celebration for a peculiarly British Olympics and Paralympics in which, almost despite itself, Britain had quite a nice time, actually.

Although it was (officially) a school and work day, London, outside of an 18th-century hanging, had rarely seen a turnout like it.

What a show they got, with Scots centre stage in several of the floats that fittingly mixed Olympians and Paralympians, all equal winners in the eyes of the crowd.

On float number eight there was Sir Chris Hoy holding aloft his two gold medals. On float 14, rower Katherine Grainger, too long the silver bridesmaid, now the happiest looking, gold medal-wearing bride in town.

On other floats the faces of the Olympics and Paralympics floated past at a regulation 2mph. Mo Farah, gold medallist in the 5000 and 10,000 metres, did the Mobot over and over for the crowd, tireless as a robot. Ellie Simmonds, with her quartet of medals, criss-crossed her float to greet the cheers on both sides. Heptathlete heroine Jessica Ennis mouthed "thank you, thank you" to the crowd, while diver Tom Daley had One Direction-style screams hurled in his direction. Jonnie Peacock, the 100m British blade runner, was cheering the crowd almost as much as they were cheering him.

Earlier, no-one could be entirely sure the crowds would come. As the bells of St Paul's signalled midday it was still possible to get a spot near the barrier. Here, the scene of last winter's anti-capitalism protests, vendors were free to roam the pavements, selling cardboard gold medals, flags and whistles. Gold medals were going for £4 a pop, a bargain considering how much Lottery money and effort went into securing the real things.

Spectators who had spent hours staking out prime viewing sites passed the time engaged in new Olympic disciplines such as marching on the spot to ease stiff legs, or doing the 100 metre sprint to the nearest Starbucks. Drop by drop, the streets began to fill up like a bathtub. Schoolchildren scuttled off buses, office workers gave up a fag break for a gawp break, Olympics and Paralympics volunteers, families from the suburbs, tourists – on and on they came.

Down in the Underground there must have been a similar snake of humanity, sweaty cheek by flushed jowl. There it was business as usual, with strangers doing anything but making eye contact. Up here in the daylight, London was most unlike London. Strangers gabbed to each other like the close neighbours they temporarily were.

Just before the parade started at 1.30pm the crowds were at least 20 deep. Such was the anticipation, everyone who passed by received a cheer, from security guards on bikes checking the route to street cleaners.

"Fair enough," said a woman from the Redbridge Ambassadors volunteer group as a street sweeper made his umpteenth drive by, "this is going to be seen all over the world."

One police officer clearly thought he was on The X-Factor, such was the way he was working the crowd. "He's a showman, isn't he," said one onlooker without a trace of sarcasm. It was that sort of good-natured day.

Union flags were the choice du jour. If there were Saltires, one would have had to have been in one of the news choppers, wielding a very big magnifying glass, to find them.

A cheery medley of police sirens signalled that the parade was coming. Motorcycle cops led the way, high-fiving members of the crowd as they passed the barriers. Next came the horses, shoes shined for the occasion. Among them was a big grey chap called Boris. A gelding, no less. The police riders, too, dispensed high-fives to the crowd. Maybe this was New York after all.

On the horizon giant blurs of colour could be seen. "It's some sort of red and blue dragony thing," shouted one expert. They were, in fact, Chinese style lions, held aloft by schoolchildren. After them came a band, and then the floats.

Instead of chariots of fire, Britain's finest came down the street in flatbed trucks of fame. Not the most glamorous means of transporting heroes, but they did the job of making the athletes visible. Suddenly, the faces on the sports pages and television screens, were up there, only feet away.

It took just under half an hour for the 21 floats to pass each spot. Bringing up the rear were the games makers, those volunteers who did so much to make London a friendlier place for visitors and home birds alike. The trucks and the keep-on-trucking brigade were on their way to a special concert on the Mall, complete with Scotland's Amy MacDonald singing Pride.

"I feel so sad, it's all over," said a woman who had spent the previous 20 minutes cheering and whooping till she was hoarse. As if heralding the end of a sporting summer like no other, that old reliable, the British shower, tapped us all on the shoulder. Time to go.

Down on the Mall, Sir Chris Hoy's wife was being interviewed by the telly. "How do you top this," asked Sarra Hoy, looking at the crowds.

Glasgow, Commonwealth Games, 2014, anyone?