When Dave Ireson, 57, realised he would be hit by extra payments for the new spare room subsidy of around £20 a week, he decided, after 30 years, it was time to move out of his family home. Since he lost his building job two years ago, the £80 weekly rent on the old three-bedroom house was being paid in full by the state.

He was reluctant to leave his home and his garden, but his children had grown up and left and he couldn't see how he was going to be able to meet the new weekly payment out of £89-a-week incapacity benefit, so he concluded downsizing was the most sensible response. Before Christmas he took a flat in what turns out to be sheltered housing 25 minutes' walk away, but because of the inconsistencies of the property market, the cost to the state of his new one-bedroom property is £113 a week. In his case, a policy designed to save money by forcing underoccupying tenants out of homes that are too big for them is costing taxpayers £33 a week more.

Pauline Gregory, 60, a former neighbour on the Bushbury Hill estate in Wolverhampton, is in the process of packing up the three-bedroom house where she brought up her children. Confronted with the prospect of paying a £20-a-week bedroom tax out of a weekly income of around £110 from April, she has also opted to leave ("I'm scrimping and saving as it is," she says); she will move around 100 miles away to Weston-super-Mare on 21 March. Her new one-bedroom flat will cost £97 a week, around £17 more than the rent on the family home where she has lived for 30 years, but this bigger sum will be met in full by housing benefit, since there will be no unoccupied rooms.

Both Gregory and Ireson are distressed at the upheaval that the new "bedroom tax" – which comes into force at the start of next month – has unleashed, and angry that their unwanted moves will end up costing the government more. Across this 1920s estate of 850 yellow-rendered houses, there are more than 150 households that will be hit by the policy. Some people are planning to move; others are calculating how they can meet the extra payments out of their already restricted budgets, so they can remain close to their families and roots. The estate managers have done a detailed audit of how families will be affected and warn that the tax will cause real hardship and an unprecedented churn among the area's usually stable population.

Pauline Gregory, who is leaving the estate where she was born to move 100 miles to a smaller property. Photograph: David Sillitoe for the Guardian

Gregory can understand the logic of freeing up a house which is too big for her, to allow a family with children to move in, but she resents being forced to leave, and is puzzled by how the enormous shift she is about to embark on will end up costing the state more. "It's stupid, isn't it," she says. The new flat has no garden, and she is leaving the vegetable patch she has worked on for three decades for new tenants. "This is what I'm going to miss," she says, examining her rhubarb, beetroot and strawberry plants. She was born on the estate, and is also saying goodbye to neighbours and friends she has spent a lifetime with. She is trying to be positive about the new stage in her life, but says she has been having panic attacks: "Pains across my chest and up my arms, wondering if I am doing the right thing or not."

Part of the problem on the Bushbury Hill estate is the design of the houses, which thwarts the logic of encouraging people to move on from homes that are too big for them. The vast majority of houses here have three bedrooms, around 100 have just two, and there are only 11 one-bedroom flats. Downsizing and remaining in the area is almost impossible. The estate figures high on national deprivation indices: about 43% of children here live in poverty and a high proportion of tenants receive benefits – even those who are working, because there is relatively little full-time work in the area.

Despite this, the estate is a popular place to live, there is usually little turnover of tenants, and rents are low. Once tenants are pushed out into the private rented sector, however, they are likely to encounter higher rents for smaller properties.

Bill Heywood, tenancy manager on the estate, believes this is a policy designed with the London property market in mind, where there is a chronic shortage of family homes and plenty of one-bedroom flats. "It doesn't work here," he says. He has been advising tenants for the past year about how to prepare for the new policy and with just three weeks to go, there is rising anxiety among those families affected. He is concerned that all the effort that has gone into making this a stable community, with little tenant turnover, will be undermined if long-term residents leave.

Overall, across the estate, the policy will save the government money, because for the moment, the vast majority of those affected are planning to stay, and will try to find the extra payments out of already tight budgets. Heywood calculates that if all the tenants stay put, the saving from the estate will be £117,429 a year.

"These are not people who can afford to save, so when the bedroom tax starts they will have to make cuts to other areas of their budget. I'm in no doubt that some of our tenants who do manage to pay their rent will go hungry at times. Others will fall into rent arrears and be at real risk of eviction and homelessness," Heywood says. A food bank has recently opened on the estate and is already busy.

The DWP says the policy makes for a fairer distribution of housing benefit, and a more efficient use of housing stock, freeing up homes for families who need them. It estimates the policy will save £930m over the first two years.

"It's only right that we bring fairness back to the system, when in England alone there are nearly two million households on the social housing waiting list and over a quarter of a million tenants are living in overcrowded homes," a DWP spokeswoman said.

Suzana, whose house has been adapted for her disabled daughter at a cost of £20,000. Photograph: David Sillitoe for the Guardian

Suzana, 54, has been living in a three-bedroom house with her son and her daughter, a few houses down from Pauline Gregory, since 2005. Her son has recently left home, which means she and her daughter are classified as underoccupying. However, since her daughter, who is 18 and has cerebral palsy, will remain living with her mother for the foreseeable future, and since their house has a through-floor wheelchair lift to take her to her bedroom upstairs, a wheelchair ramp to the entrance, and a wheelchair-accessible bathroom built out the back at a cost of around £20,000, the prospect of leaving the house is very unwelcome. If they stay, Suzana will have to pay an extra £11.59 a week, which she thinks will have to come out of her food budget.

She is worried about how she will find the extra money if she stays and how easy it would be to find another flat with similar adjustments. Finding any kind of property in the private rented market will be difficult; according to Shelter, under 50% of private landlords accept tenants on housing benefit.

"We talk about it – is it harder to stay or harder to move?" Suzana says. They remain undecided. Their dilemma reflects the difficulties being experienced by the families of 10 disabled and vulnerable children who this week issued judicial review proceedings against the secretary of state for work and pensions, Iain Duncan Smith, challenging the policy on the grounds that the regulations have "failed to take proper account of the needs of vulnerable children".

Around the corner, Peter Inscoe, 46, an unemployed sign-maker, is determined to stay in his house. He has 20 years of experience in the sign-making industry, and is also a talented illustrator, and remains reasonably confident that he may find new work. Born on the estate, he was allocated a three-bedroom house as a single person 12 years ago, at a time when there was little demand for the properties here. His rent has only been paid by housing benefit since he lost his job three years ago. If he finds work, and is able to meet the £80-a-week rent himself, he would no longer be under pressure to move.

Peter Inscoe: 'I'm going to cut down on food shopping. I'm dreading it.' Photograph: David Sillitoe for the Guardian

Quite how he will meet the £20 bedroom tax out of his weekly jobseekers' allowance of £71 remains unclear. He is already frustrated by requests from his doctor to eat more fruit and vegetables to help combat his diabetes, pointing out that this is hard on his budget. He has decided give up his fortnightly bus pass (£23.30), which will make getting to job interviews more complicated because it is a three-mile walk to town. "I'll be stuck much more at home and I'm already climbing the walls," he says. "I'm going to have just under £51 to pay all the bills and buy everything I need. I'm going to cut down on food shopping. I'm dreading it."

Inscoe would rather eat less than move away from neighbours he has known all his life. He also points out that if he moved, most one-bedroom flats in the area would be more expensive, so the decision could end up costing the state more. "The government would have to pay for it because I wouldn't be underoccupying," he says.

He is also puzzled by why the pensioners who live in the houses around him are exempt from the tax. "If it was really about dealing with underoccupation, the government would be dealing with the biggest group of underoccupiers – the pensioners," Heywood says. "But it would be electoral suicide to start turfing out pensioners. It is politically expedient to tackle this area; it fits the scroungers and skivers agenda."

Another of those affected is Stacey Poulton, 21, a single mother with a two-year-old boy and a three-year-old girl. Nationwide, nearly a quarter of those to be affected by the tax will be single parents, according to government figures indicating that lone parents make up 150,000 of the 660,000 people who are expected to have their benefits reduced, by an average of £13 a week (£676 a year). Poulton lives in a three-bedroom house, and currently each child has its own room, but under the regulations, children of different sexes should share a room until they are 10 so technically they are underoccupying. If she could swap to a two-bedroom house, she would (not least because two and three-bedroom houses on the estate are exactly the same size, but have just been converted differently) but since there are so few two-bedroom houses in the neighbourhood, and since her mother, grandmother and great-grandmother are all neighbours, she has decided to stay put. From April she will be paying £44 a month in bedroom taxes.

Stacey Poulton with two-year-old Dylan. Photograph: David Sillitoe for the Guardian

The tax is a subject that has been troubling a lot of the mothers at the local children's centre. "Some of the mums are saying that they are going to have more kids just so they don't have to pay. It's ridiculous, but I think there are going to be loads of extra children because of this," she says.

David Scriven, 58, would also like to move to a two-bedroom house, and give up the four-bedroom home where he and his wife, Janet, brought up their six children, but he is also stuck because of the absence of two-bedroom homes in the area. Only their 17-year-old son remains living with them, so they are classified as underoccupying by two rooms, and if they don't move, they will also be charged about £21 a week. The couple are looking at home-swap schemes and are beginning to contemplate how they will dispose of belongings accumulated over 34 years of married life, in order to downsize. Janet is wondering how much it will cost to bubble-wrap all the glass ornaments, and the framed photographs of their six children at various stages of development which cover the wall.

Although both work, they only have part-time jobs; David has not managed to find a full-time job since 2002 when Schneider Electric, a local employer, laid off large numbers of staff, and is working part-time in the freezer department of the local Co-op; he has not been able to increase his hours, despite requests to switch to a full-time role. Janet works as a dinner lady at the local school. Their combined income is low so currently they receive housing benefit.

David Scriven is contemplating a move from the home where he and his wife brought up six children. Photograph: David Sillitoe for the Guardian

If they could find the money to stay there for a few years, until retirement age, the couple would no longer be obliged to move because pensioners who remain in the family home once their children have left are unaffected by the policy and can continue to underoccupy. As it is, they hope somehow to stay in the area, allowing them to remain in their jobs and be close to three of their children who still live on the estate.

"How are we going to pay our bills if we're down £84 a month? We have to find the money somehow or another because if we can't find it, we'll be threatened with the courts," he says, adding that the process has made him feel like jumping under a bus.

Dave Ireson, who moved before Christmas, says he has also been made to feel suicidal by the move from the estate where he had lived all his life.

He moved to a sheltered complex for the elderly and vulnerable 25 minutes' walk away. He is by some margin the youngest person in the block and feels so isolated that he has only left the flat five times in as many months. "They say come down to the fun room but you have to sit there with 80-year-old men playing bingo," he says.

He had hoped that the move would be positive, but he hates his new flat, and misses his old house. "It was my home. The house was full of memories for me; all my history was there; my friends and children are nearby," he says. "But I didn't want to be in a situation where I couldn't afford the rent."

He says his mental health has been damaged by moving. He describes Bushbury Hill as a "tough estate, but people are very close. There were people I could go and sit with.

"Here, you haven't got anybody around you to support you. It's not good for me here. I try to spend as much time as I can sleeping in the day, so I'm not sitting in this room all day," he says. "It's costing more for me to be here than when I was in my own home and happy."

• This article was amended on 31 March 2014 to remove personal details of one the people interviewed.