Trooping the colour is the biggest annual event in the calendar of royal pageantry. On the second Saturday in June, the entire British royal family gathers in London to celebrate the Queen’s official birthday. The ‘colour’ (the flag of one of the royal regiments) is ‘trooped’ (paraded) along the Mall from Buckingham Palace to Horseguards Parade in a vibrant display of military tradition, impeccable horsemanship and silly hats.

This year’s trooping the colour had the extra benefits of perfect weather and being Meghan Markle’s first public outing since her marriage to Prince Harry. Even non-royalists might find that combination hard to resist. My partner and I, on holidays from Australia, were staying less than half a kilometre from the action – a mere ten-minute stroll away.

Unfortunately, we didn’t get the memo, and spent the whole sunny morning shopping in Oxford Street. Oops. But we did get to witness a different kind of parade later in the day.

This year, the second Saturday in June was also the day of the World Naked Bike Ride, when thousands of people shed their clothes and take to their bikes to draw attention to the vulnerability of cyclists in our car-dominated cities. Do you normally have trouble noticing cyclists on the road? Not on this day.

The London chapter of the WNBR organized six different routes, which converged on Hyde Park during the late afternoon of 9 June. We found ourselves inadvertently in the thick of one cohort of naked cyclists, when we took what was supposed to be a shortcut along Shaftesbury Avenue, trying to get away from the hordes of pedestrians at Leicester Square. It was a case of out of the frying pan and into the fire.

Seeing hundreds of naked people in the street without forewarning is startling. There were so many of them, they were all headed our way, and they were, for the most part, so very naked. It was a little bit like the Summer of Love, and a little bit like Hieronymus Bosch’s painting of The Last Judgement.

What with red lights, young men leaving the ranks to pose for selfies with girls on the pavement, and the general quantity of bikes and bodies, the parade made slow progress.

Of the naked cyclists near us, I estimated 90% were male. While many of the relatively few women had chosen to wear underwear or body paint, most of the men had opted for the full monty. It was quite an eye-opener. Who knew the human form came in such shapes and sizes?

Later I read that the event meant something, or some things. It was intended to be a protest against our society’s oil-dependency and (also) a celebration of the human body. For an accidental spectator it felt more random than that, a piece of authorized anarchism in the spirit of Carnival. Kings for a day, the naked cyclists ruled the roads by committing a mass act of indecent exposure.

‘Look at us,’ they were saying down on The Mall. ‘We are the British royal and military establishment, and we’ve got tradition.’ ‘Look at us’, the cyclists replied. ‘We’ve got balls!’

The next day, Sunday, we got caught up with two more parades. In the morning, we followed the sounds of laughter and cheering to Piccadilly, where 30,000 women were marching to commemorate hundred years of British women’s right to vote.

Women of all ages were there, many dressed in the suffragette colours of purple and green. It was a joyous, heartfelt occasion, part celebration, part call to action in the ongoing struggle for gender equality.

In the early evening, in the same part of London, we passed police officers in bulletproof vests, some on horseback, some running, some speaking urgently into walkie-talkies. They were monitoring two political marches that almost crossed paths, but didn’t quite. A small number of anti-Hezbollah protestors were marching under an Israeli flag, while a larger number of anti-Israel protestors were marching under ‘free Gaza’ banners and (controversially) Hezbollah flags. The atmosphere was tense, bystanders looked stressed, and we didn’t linger.

So, all in all, we saw a lot of things trooped in London that weekend – bare bottoms, suffragette banners, warring flags. Smiling faces, scowling faces, pride, mischief, rage.

Just not the famous colours.