The queue to get onto the train at Howard University subway station stretched all the way up the stairs and onto the street. As I approached, women began to turn around, looking at us and shaking their heads: ‘Don’t bother.’ I decided to walk the two miles to the National Mall. Washington DC is hard to navigate; it is laid out in a series of pinwheels designed to be difficult to invade, and many areas are geoblocked, turning the map on my phone into a blank. But there was only one direction that anyone was walking. Protesters held signs and wore ‘pussy hats’; pink, mostly handmade, with points on the top like cat ears. A lot of us were carrying clear plastic backpacks with granola bars and bottles of water; fabric bags weren’t allowed because they are too easy to hide a bomb in.

It’s not certain how many of us there were at the Women’s March on Washington on Saturday. The DC authorities say 500,000, almost certainly too low, and the protest organisers say 1.1 million, almost certainly too high. At any rate, more than attended Donald Trump's inauguration. The crowd overwhelmed the small city, and packed its streets for most of the day. At the Mall, the crowd was so dense that it was impossible to reach the main stage near the Capitol, where Scarlett Johansson and Janelle Monáe gave speeches along with Angela Davis and Gloria Steinem. The crowd stretched about ten blocks back from the Capitol building, thinning out in front of the Smithsonian.

People raised signs over their heads and held their phones up to take pictures. The most frequent were ‘NASTY WOMAN’ and ‘PUSSY GRABS BACK’. ‘WE SHALL OVERCOMB’ one said. Another: ‘CAN’T GRAB US ALL, YOUR HANDS ARE TOO SMALL.' A striking number of the signs were in Russian, or referenced Putin: ‘JUST SAY NYET TO FASCISM!’ A thin woman with dark hair held a sign that said: ‘феминистка’. There were people in costume: a middle-aged couple wore matching Darth Vader masks and robes, with puffy orange wigs glued on top of their plastic helmets.

Young men lifted their girlfriends onto their shoulders to take pictures or scan the crowd for lost friends: ‘Oh there they are! I see them!’ The crowd was as dense as on a commuter train: heads pushed into strangers’ shoulders, backpacks scraping the arms of passersby. Women pushed prams haltingly through the crowd, almost all of them with the same joke: ‘I’m parting the Red Sea!’ It was impossible not to step on someone’s toes. There was a constant soft chant of ‘Excuse me … Sorry … Pardon.’

The Women’s March on Washington began as a Facebook post in the days after Donald Trump’s election, and gathered steam in the weeks that followed as the incoming administration doubled down on its conflicts of interest, draconian demands for cuts to social services and proposals for ethnic cleansing. By Christmas, it was the main event for anti-Trump resistance organisers, with sister marches organised in all 50 states and around the world.

A black girl, maybe nine years old, appeared at my elbow; she was grinning, pushing her way forward. ‘I want to see a sign this big that says “Black Lives Matter”,’ she said, and threw her arms out as far as the tight quarters would allow. The elderly white woman accompanying her took her hand. ‘Let’s go see if we can find one.’

The crowd was overwhelmingly white. This may have been partly the fault of the event’s organisers, whose well-intentioned attempts to foster racial inclusiveness were nonetheless clumsy. One poster for the event featured a raised black fist on a mint-coloured background, above the slogan ‘HEAR OUR VOICE’. The fist was held by white and brown hands, clutching it at the wrist. The message was meant to be that white women would attend the march in solidarity with women of colour, but this didn’t really come across. If anything, the black fist looked like it was being dragged down.

Because the march was supposed to be inclusive, positive and accessible to the mainstream, the mood was almost aggressively chipper. Everywhere, people were laughing; signs were gleefully irreverent: ‘FAGGOTS AGAINST FASCISM’; ‘TRUMP HAS A TINY PENIS’. It was like a rock festival. The optimism at times felt naive, or even wilfully ignorant, in the face of the dangers facing America’s racial minorities.

On Constitution Avenue, the crowd parted and headed in different directions. Some of us surged north and west, towards the White House. Chants began: ‘WE ARE THE POPULAR VOTE’; ‘YOU WORK FOR US NOW’; ‘WE WANT A LEADER, NOT A CREEPY TWEETER.’ A group of black teenagers began yelling ‘BLACK LIVES MATTER’ and the marchers joined in; two young men started to dance. Scattered throughout Washington that day were anti-choice demonstrators, who arrived with megaphones and large banners showing aborted foetuses. Whenever the crowds approached them, a chant rose of ‘MY BODY, MY CHOICE’. Men added quietly: ‘Her body, her choice.’

The street as we approached the White House was filthy with manure from the horses in Friday's inauguration parade. Cardboard had been vainly thrown over it in places, but thousands of marching feet dragged it across the road. A smattering of Trump supporters in red hats stood at the kerb, watching us go by. A heavily made-up white girl, maybe 14, stood with her mother, both of them wearing matching blue sweatshirts with the new president’s face on. ‘Loooo-sers!’ she called out at us while her mother rubbed her shoulder, ‘loooooo-sers!’

People left their signs outside the White House gates, hundreds of them lined up along the ground. The crowd was still thick: several thousand of us were staring in at the fountain and the white pillars. I was surprised by how small the White House is. It could be a stately home or a school. There may never be so many of Trump’s enemies outside it again, and I wondered how easy it would be for all of us to walk in and take it for ourselves. I pictured myself pushing the orange toupee off his head with my index finger, flopping into his high-backed desk chair and spinning around. Instead I stood outside and peered at the door from the wrong side of the black iron fence.