“Look!” shrieks the young woman standing next to me on the platform. “A mouse!” It’s 2.30am at Green Park underground and the Jubilee line Night Tube has been open for two hours. “I’m not normally out at this time,” she says, “but I’ve just handed in my dissertation and I’ve had a few drinks.” I’m tempted to tell her that I can see that. Instead, I ask her if she feels safe. She looks around and shrugs. “Everyone,” she says, “is about my age. I am,” she adds, looking down at the tiny creature nuzzling a crisp packet, “more scared of that”.

On one thing, at least, the young woman is right. Most of the people travelling on the Jubilee line in the early hours are young. Most of the people travelling on the Central and Victoria lines are, too. The atmosphere is cheerful. “I feel very safe,” says a young woman in a red beret. “Me too,” says her friend. They have both just started at University College London and have been living in London for two weeks. A young Latvian woman on the Central line is more cautious. “I feel safe on the Tube,” she says, “but not in East London, where I live.”

The Jubilee line Night Tube, which runs for 24 hours on Friday and Saturday nights, opened on 7 October. The Central and Victoria lines have been running a weekend night service since 19 August, after more than a year of strikes and delays. The Northern line Night Tube opened on 19 November and the Piccadilly line is due by the end of the year. This is, says the Mayor, Sadiq Khan, all part of the plan to make London a 24-hour city.

The new services, which will cut night-time journeys by an average of 20 minutes, will, according to his office, support about 2,000 permanent jobs and boost the city’s night-time economy by £77 million a year. Cultural leaders have rushed to praise it. So have the owners of nightclubs and bars. It is, of course, bound to boost the economy and bring a buzz to the city. But is the 24-hour city good for women?

Cities are different at night. As Matthew Beaumont explains in his fascinating book Nightwalking, night was traditionally associated with “vagabonds, robbers, ghosts, demons”. Until street lighting arrived in London at the end of the seventeenth century, the night “retained its ancient biblical and mythological associations with anarchy, chaos and evil”. But in darkness, or at least a darkness punctuated by a few streetlights, there can also be a kind of liberation. At night, argues Beaumont, drawing on accounts by the poet John Clare and the essayist Thomas de Quincey, “one can be someone and no one at the same time”. It’s a view echoed by Virginia Woolf in her essay Street Haunting. “The evening hour,” she says, “gives us the irresponsibility which darkness and lamplight bestow. We are no longer quite ourselves.”

I don’t agree with Virginia Woolf about all that much, but I do agree with her on this. I love London at night. I’m used to roaming the streets at night as I never get cabs and don’t live near a Tube. I’ve lived in London for 30 years, sometimes in some pretty ropey areas, and I’ve rarely felt unsafe. But many women say they do.

Women alone on the streets of London at night have traditionally been defined in relation to men. In the popular imagination, says Beaumont, they are “either predators in the form of prostitutes” or “the potential victims of sexual assault”. I have had my handbag stolen six or seven times. This has certainly made me feel vulnerable as a handbag-owning creature, but not particularly as a woman. But while I was out and about researching this piece, I had a couple of mild shocks. Renewing my Oyster card at 3.45am, I suddenly found that a man I had spotted on the other side of the street, and who had set off mental alarm bells, had followed me into an empty station. Before I could tap in my PIN number, I grabbed my card and marched away.

At Stockwell Tube at 3am the following night, a young man who stank of drink grabbed my arm and asked if “my husband” was happy about me being out at night on my own. I told him I didn’t have one and gave him a little lecture, but found myself thinking of the young cleaner I had interviewed at the bus stop at 4am the day before. “I believe in God,” she said when I asked her if she felt safe travelling in the dark. “I know it’s not safe, but God protects me.”

The Met’s press office told me that it would take three weeks to provide breakdowns by gender of crime victims in London, so these are clearly not statistics that they are often asked to supply. But there isn’t much doubt that the majority of crimes committed at night in London are “acts of violence”, often alcohol-fuelled, by men against men. Last year, there were about 233,000 “acts of violence” in London. There were 5,827 rapes and 11,046 crimes categorised as “other sexual”. Almost 90 per cent of rapes and sexual crimes are committed against women. In a city of 8.7 million, where 31 million journeys are made on the transport network each week, the odds of being assaulted as a woman are actually pretty low.

For sex workers, they are much higher. According to the English Collective of Prostitutes, there are about 42,000 sex workers in London. Research from the University of Leeds in 2015 found that 47 per cent of sex workers have been victims of crime. Of the 941 reports of violence gathered by National Ugly Mugs, a reporting scheme for sex workers, only a quarter said they would share the full details with police. This, clearly, is one group of women who don’t feel the police are on their side.

On a 4am bus trip into town, most of the women I talked to said they felt safe on buses “because of the cameras”, but much less safe on the streets. Most were off to do cleaning jobs. Most were reluctant to talk. And very few were white. There were one or two white British revellers, on their way home after a long night clubbing, but the early morning code is silence. Many of these women – and men, who far outnumber the women on the buses – will earn about £20 for a three-hour shift.

Illustration by Lucinda Rogers

Sitting on a bus full of workers yawning in the dark is a stark reminder of what it takes for a city to run. And that’s just what it takes for a city to run in the day. At an unexpected overnight visit to A&E last week, it was fairly clear that a 12-hour night shift wasn’t the best way to cheer anyone up. It also isn’t good for your health. There are about three million night workers in this country, about 370,000 in London. Of these, according to the TUC, 60.6 per cent are men and 39.4 per cent are women. Night shifts increase the risk of cardiovascular disease, diabetes and depression. They can, according to the TUC, cause relationship problems and affect the emotional wellbeing of night workers’ children. They can, in other words, come at quite a price.

There are other prices to be paid for the 24-hour city. You probably won’t love it if you live next door to a noisy nightclub or pub. You might not like it if you’re a police officer or health worker having to deal with large numbers of people who are drunk. But if you’re someone who loves the buzz and thrum of a vibrant world city, or even just nipping out, as I did, to have a cappuccino at Bar Italia in Soho at 3am, the 24-hour city feels like sheer, pure, stress-busting fun.

The Night Tube is helping. Uber is helping, offering swift, safe travel at the tap of an app. Organisations like Hollaback, set up to tackle the sexual harassment of women and girls, are helping: Hollaback offers training in ‘bystander intervention’ in schools, pubs and clubs. And the Mayor of London is helping, investing £3.4m in 100 British Transport Officers “to enhance the police presence at night”. He has appointed a Night Czar “to help oversee the transformation of London as a 24-hour city”.  He is, his office told me, “committed to doing everything possible to tackle violence against women and girls”.

Well, that’s quite a promise, and let’s hope it’s true. Like many Londoners, I love the idea of the 24-hour city. I live on a busy high street where quite a few shops are open all night. If I wanted a quiet life, I would live in a village. I don’t want a quiet life, but I do want a safe one. I want women in London to be able to walk around without being followed into dark corners or asked if their husband has allowed them out. I want women to be able to sit on a Tube platform at 3am and not have their arm stroked. I’d like to think that things are getting better, but when Donald Trump can call boasts about sexual assault “locker room talk”, it’s clear that there’s a long, long, way to go.