Thousands of people joined a demonstration in London ending at Downing Street on Saturday in protest at what they say is the crisis facing the NHS.

Bearing placards with slogans including “more staff, more beds, more funds”, and “Saving lives costs money, Saving money costs lives”, they chanted “Keep your hands off our NHS” as they set off from Warren Street at lunchtime. The demonstration, called “NHS in crisis: Fix it now”, was organised by the People’s Assembly and Health Campaigns Together. Marchers were addressed by speakers who outlined their experience of the pressures facing the NHS. One mother told how her daughter died after she had been allowed out of psychiatric care too soon.

Nicky Romero sobbed as she told of the death of her daughter, Becky. A coroner found Becky’s suicide was linked to NHS failings after the 15-year-old was discharged from a psychiatric ward, despite self-harming on the same day and her parents’ pleas that she be kept in hospital.

The schoolgirl died in July 2017. “What kind of future will our children have if they can’t get the help they need?” her mother asked. “If the NHS was properly funded my daughter might still be alive.”

Jon Ashworth, the shadow health secretary joined the march and said this was the worst winter the NHS had experienced, blaming government austerity measures.

Ralf Little, the actor who has challenged health secretary Jeremy Hunt to a public debate on the health service, was cheered when he told the crowd that the NHS was the envy of the world. He had previously told how his mother was saved by NHS treatment for free when she suffered a stroke. Little said the quality of the NHS was threatened by underfunding. “It’s a political choice to leave patients sleeping in corridors,” he said.

Cecilia Anim, president of the Royal College of Nurses, told the crowds there were 40,000 nursing vacancies around the UK and the shortage was affecting service delivery. “I’ve never in my 40 years in nursing seen anything like this,” she said.

Tamsyn Bacchus, a Save Lewisham Hospital campaigner, said she feared the UK could morph the NHS into a US-style user-pays health service. “I have faith, and so do all these folk here, that it’s so important that when you are ill, when your child is running a high fever, when you need the hospital or a doctor, you can get them without worrying about having to pay for it.”

In response to the rally, the Department of Health and Social Care said: “We know the NHS is extremely busy, which is why the government supported it this winter with an additional £437m of funding, and why it was given top priority in the recent budget with an extra £2.8bn allocated over the next two years.”