As soon as Marissa was old enough to walk, she started caring for her mother. Suzanna, 51, was left with severe spinal damage and arthritis on top of long-term breathing problems after two car accidents. The five-year-old helped her disabled mother to get to their third-floor flat in a block with no lift: she would hold her mum’s hand as they went up, step by step – all 150 of them. Marissa would bring her water and do the laundry.

She would even try to help cook tea: dry pasta and tomatoes. “Marissa would say, ‘Mummy, you have a mouth full of hands, let me help’,” Suzanna says. “She meant, ‘you’ve got your hands full’.”

Now 11, Marissa is only a few months into “big school” but is on call for her mum 24/7. Three years ago the council gave Suzanna an allowance for eight hours’ care a week from a personal assistant, but it’s nowhere near enough. Marissa picks up the slack, helping her mother get out of bed in the morning, and chipping in with the washing up, cleaning, cooking and shopping.

“She amazes me,” Suzanna says.

When Boris Johnson announced his new immigration plans last week to cut “unskilled” visas – said by unions to spell “absolute disaster” for the care sector – it’s unlikely he was thinking much about Marissa. Local government is currently scraping the bottom of its coffers, and there are 122,000 social care vacancies, meaning both social care packages and the staff needed to provide them are already scarce.

Who’s filling in the gaps? In part, young carers like Marissa. Figures suggest there are 700,000 in the UK, though that’s likely to be just the tip of the iceberg. Research by the charity Action for Children this month finds young carers are quietly doing the equivalent of £12,000 worth of unpaid work a year. “Young carers” is a tellingly sanitised term – a euphemism for child labour. We normalise it, accepting working conditions for children that would not be legal outside the home.

Now, even a break is too much to ask for. A decade of austerity means that not only have social care packages shrunk, but so have the budgets for respite centres. Services across the country designed to give kids a rest have closed their doors, while many run by charities like Action for Children have been taken back in-house by councils and run as a skeleton services – often with no transport or outreach capacity for hard-to-reach families.

Child carers are not an anomaly of the social care crisis but a grotesque example of a bigger scandal, in which the state withdraws responsibility and the burden falls on already struggling families.

In new research by the MS Society, one in six family carers say they are now providing more than 90 hours of care every week as cash-strapped local authorities withdraw their provision. For their trouble, the government provides £66.15 in carer’s allowance per week – which works out at about 73p an hour. Their reward? A higher chance of living in poverty and with mental and physical health problems because of the toll of caring. The MS Society study shows a third of respondents have had to give up work to care for a loved one – and these are largely women.

If the human impact isn’t enough, consider the economic case. Unpaid carers giving up work early to provide this support costs between £3bn and £6bn in lost tax every year in England. Migrant care workers are a lifeline for a service that is flatlining. Four in 10 care workers in London are from overseas – and yet Johnson’s dog-whistle immigration plans dare to call them “unskilled”.

The home secretary, Priti Patel, offered the solution of replacing migrant workers with “economically inactive” people, but they turned out in reality to be largely the long-term ill, those who had retired and – you guessed it, those already taking on unpaid caring responsibilities.

Ministers have long tried to shift the social care burden on to families. In 2018, they launched a new “big society” initiative as bankrupt councils were told to lean on relatives and neighbours to meet their legal duty to disabled and older people. Get ready for more of this rhetoric in the coming months as the government finds out what “taking control” really means for the crumbling care sector.

But the case for immigration cannot be made by weighing up what migrants can do for the rest of us. The demands for both a humane immigration and social care system come down to the same point: we are human beings with intrinsic worth, who deserve dignity and respect.

It is only by valuing the labour of carers that ministers will provide what is needed: a real investment in social care, support for family carers and a more welcoming attitude towards migration. When children are left to clear up the state’s mess, the government has truly failed.

• Frances Ryan is a Guardian columnist. Her book, Crippled: Austerity and the Demonisation of Disabled People, is out on audiobook now