Since this era of financial austerity began, newspapers and magazines have hurried to publish advice on how to get by on a straitened budget. So here is one to beat all others. Today we offer a guide to surviving on under £10 a week. Without a roof over your head! Without a bed to lie on! With no support from family or friends!

It's quite possible, and here's how. These helpful tips come from four failed asylum seekers in Birmingham, who remain in this country, preparing to appeal the Home Office decision, sleeping meanwhile in hedges, doorways, old garages and staircases.

Abdi, 34 Somalia

It would be wrong to describe Abdi as poor because this suggests he doesn't have enough money to survive on, which would be to put a rather optimistic spin on his situation. He isn't poor, he just doesn't have any money at all, and hasn't done for the last six months since his asylum claim was rejected in December.

He is pragmatic and uncomplaining as he explains how he manages to subsist beyond the fringes of society, hand to mouth, on meals of bread and tuna bought with Red Cross food vouchers. He has noticed, however, that the longer he lives like this, the heavier the toll on his health.

The Red Cross today publishes an uncharacteristically hard-hitting report attacking the "shameful" way the British immigration system treats those whose claims for asylum have been denied, and who have yet to return home. Once an application is turned down, the asylum seeker loses all eligibility for accommodation and financial support. Estimates suggest that there are about 200,000 asylum seekers who receive no state support, of whom perhaps 20,000 are surviving on food provided by the Red Cross or other charities. The organisation compares this emergency aid distribution to the work it does in Sudan, and is calling for the government to adopt a more "humane" approach.

Once you lose your home and financial support, the priority is to find somewhere safe to sleep. Abdi has three places he sleeps regularly, and he rotates them according to weather conditions. The first is in a mosque in a suburb of Birmingham, particularly useful when there was heavy snow. To stay there, you need to go to last prayers, join the worshippers for a while and then slip away and shut yourself in a toilet cubicle. Shortly afterwards the lights are switched off and the building locked up, and there is a secure place for the night.

Anxious to avoid suspicion, he doesn't risk staying there too often. So he has also been sleeping intermittently on a flattened cardboard box at the top of a concrete stairway to a block of flats nearby. This place is sheltered from the rain, and it has the added advantage of a light bulb that can be left on or unscrewed when he wants darkness, but the neighbours are not tremendously welcoming, and he tries not to get there until he calculates they will all be asleep. When they see him, they are generally abusive and threaten to call the police. Someone has scratched "Your Dead" into the side of his cardboard container, which he has left leaning against the wall.

"They're just joking with me," he says amiably.

The third place is in a narrow alleyway between park railings and a row of back yards, a few streets away. He has hidden his sleeping bag (marked "Don't take it. Please. Homeless") underneath a heap of discarded building materials, wooden planks with protruding nails, and broken mirrored glass. The adjoining section of park is a place where teenagers hang out to take drugs in the evening, so most people prefer to avoid the area, which means he is mostly left undisturbed.

For food he goes to the Red Cross every Tuesday, where he queues up for £10 worth of Morrison's vouchers, usually alongside up to 100 other failed asylum seekers. Volunteers here used to distribute emergency handouts of £15, but funding shortages forced them to reduce this to £10. The recipients did not protest, says Joseph Nibizi, manager at the destitution clinic; they are desperately grateful for whatever help they can get.

'People say "Go home" or "Get a job". I can't do either'

Although Birmingham has a large number of destitute asylum seekers they are not very visible. They do not sit at train stations or by cashpoints; instead they linger in the shadows, afraid of attracting attention from officials.

Abdi cultivates invisibility. He spends his day pacing from one spot to another, afraid to loiter too long, worried that people will think he is a criminal. He doesn't approve of begging. He is prohibited from working, and does not want to try working illegally – washing cars at the traffic lights – for fear of jeopardising the fresh claim for asylum he is preparing.

Existing without any money naturally causes logistical problems. Tomorrow he has to travel to Solihull on the outskirts of Birmingham for his monthly registration with the Home Office, and the bus fare will cost £3.50. He visits Morrison's to see if he can get change from his vouchers, but he knows from previous visits that the cashiers are not very well disposed to asylum seekers, and will only give change if at least half the value of the voucher is spent. It seems a trifling point, but since the change from the Morrison's voucher represents the only coins that pass through his hands during the week, it is of critical importance.

As he walks through the 14 aisles of the vast supermarket, he waves towards the shelves full of food and says: "I pass everything by because of my budget." He buys some discounted sliced bread, four tins of tuna chunks, four small tins of baked beans, and a litre of milk. He doesn't own a tin opener, but a nearby cafe owner usually agrees to lend him one, and he eats whatever he buys cold.

(At the till there seems to be some inconsistency about the policy on giving change from tokens. A cashier is happy to give me £4.50 change when I give her one of the £5 tokens to buy the 50p loaf of bread. A manager I check with smiles and says I can spend as much or as little of the £5 gift token as I like. When Abdi asks another cashier, he is told he must spend at least £2.50.)

Abdi pours out stories from his existence on the streets; they are not very cheerful, but he tells them with a sense of humour, outlining the absurdity of his situation. He has a story about a young woman who befriended him on a bench; after several days of sympathetic visits from her, it transpired that she was merely attempting to recruit him to deal drugs in the park. He has another story, told equally cheerfully, about a family who set their dogs loose on him in the alleyway where he was sleeping.

It is a bleak existence, but he is not inclined to return to Somalia. He won't say much about what prompted him to flee through Africa and then Europe hidden in cars and lorries, commenting only: "If you understand that it is a choice between living here in this way and going back to be slaughtered, then you understand that there is no choice."

His original asylum claim was refused by a judge who described it as "not credible". Campaigners point out that the asylum system is not wholly reliable, characterised by a "culture of disbelief", the onus being on asylum seekers to prove that they are not lying. Last year, 28% of people who appealed against refused asylum cases were granted leave to remain, a figure that campaigners say reflects serious flaws in the initial decision-making process. Besides, whether or not someone's claim is legitimate is not relevant to the question of whether they should be forced to live on the streets, campaigners argue.

The Red Cross is responding to the humanitarian needs of people who have nothing and nowhere to live, and staff members do not attempt to judge whether their clients' claims are solid or not. "We are a humanitarian organisation, and we believe that people run away from persecution. It is for the government to decide whether they have good cases or bad cases," Nibizi says.

Abdi has a meeting with a Home Office official later this month to go through his appeal submission. It is increasingly hard to find a solicitor, especially if you have no money. The UK's leading asylum charity, Refugee and Migrant Justice, announced yesterday that it was going into administration because of funding shortages, due to government delays in the payment of legal aid. If he submits an appeal, and it is accepted by the Home Office as potentially viable, then he will be eligible for hardship support payments and housing, but it is difficult to secure that status. Until then, he exists in limbo.

It is a confusing situation to understand. Abdi is not here illegally, since he is going through all the correct legal hoops, registering his presence with the Home Office every month, and until he gets served a removal notice he is not breaking the law by staying. He is at pains to do everything correctly, abiding by the stipulation not to work, determined not to break the law, even if that means surviving in a gutter on ad hoc charity handouts.

"Criminals in your prisons still get their basic needs. What about people who come here searching for safety?" he asks. "If they deny these things, do they want us to die? Or do they want us to break the law? When people see me sleeping in the stairway, they say 'Go home' or 'Get a job'. I can't do either."

Abdi is careful not to express any hostility towards the government for its policy, but Nibizi is angry. "You can remove people back to their home country, or you can keep them here. But you have to give people food. It is inhumane not to give people food. You cannot starve people out of the country," he says.

"Nowhere else is providing the kind of support [the Red Cross does]. Ten pounds is not enough to live on, but it can sustain them until someone else can help them. Our service is meant to be an emergency response, but the government is not dealing with them. We can't leave them to die outside."

Haile, 32 Ethiopia

These attitudes towards asylum seekers are on display among a group of 40 or so homeless people sheltering from the rain on the ground floor of a multi-storey car park in the city centre, waiting for soup and sandwiches to be distributed by volunteers from a Baptist church.

One tall, white man in his 40s is expressing loud anger about the decline of the country. A few years ago, he remarks, there would have been no foreigners queueing up at these soup kitchens. "It was just the English," he laments, adding that the outsiders should be sent home. "If they try to come back, their passports should be taken away and they should be sent to prison."

Haile, who has been living homeless in central Birmingham for five years, since being released from an immigration detention centre, does not respond. "He's always like that. He says, 'English first for food.' I don't pay any attention to him. He drinks," Haile says. On the whole, he avoids telling people about his background. "If they knew I was an asylum seeker," he says, gesturing to the group, made up mainly of local drug addicts, alcoholics and the mentally ill, "and that I don't have papers to be in this country, I think I would be dead now. I don't make friendships with anyone; I don't know who is good or bad."

He lives alone, in conditions similar to those we see in news reports highlighting the plight of survivors whose lives have been torn up by faraway natural disasters before the major aid agencies have arrived – no electricity, no shelter from the elements, no sanitation, no water, no food, no mattress etc.

For over a year now, he has been living in a fenced-off doorway, at the back of an expensive hotel in the city centre, by the entrance to a now defunct car park. Local authorities have tried to block the way in, erecting a sheet of chipboard marked "Trespassers will be prosecuted" over the gap he used to squeeze through. Now he has to climb a 10ft metal fence with flattened prongs at the top, and slide down on the other side, where there is a space in the old doorway, covered from the rain.

It has been raining a lot, so it is difficult to get over the fence which (since he is a little short) is over twice his height. He puts his trainers on two black-painted railings, legs apart, and tries pull himself up. There is a slipping noise of wet rubber from his shoes and he fails to get over. He slips down the railings and tries again. It is painful to watch.

"This is my sleeping bag, my table, bed, blanket," he says through the fence, once he has made it to the other side. "My toilet," he says, pointing to a dank corner. "My clothes," he adds, nodding towards a heap of crumpled clothes and shoes. Piles of rubbish have been thrown through the railings by passersby - McDonald's yellow polystyrene containers, Sprite and Quavers packets, KFC and Red Bull, cigarette packets.

Haile says he has rat problems and fox problems, but is upbeat about the place he has found. The difficulty of getting in gives him a sense of security once he is inside.

"Sometimes I look and think it's like a prison, it's like a cage. But no one can throw stones at me here," he says. "This is my mansion. I'm a rich man. I own this hotel. If you want a room, I'll rent it to you cheap, cheap."

The strain of living in these conditions has taken a toll and Haile is clearly struggling to cope with life. Immigration letters in brown envelopes (delivered to the Red Cross and passed on to him) lie strewn in between the clothes. Taken by his parents from Ethiopia to Tanzania as a baby, he came here as a stowaway on a boat in 2000. Several asylum applications have been refused, and he is under instructions to return to Tanzania. But he is not clear whether he would be accepted there, since it is not his original home. He has no capacity to get himself there, and one attempt to deport him forcibly was cancelled at the last moment several years ago, since when he has been left to forage for survival in central Birmingham.

"My life is wasted. My parents died. I don't have parents. I don't have a country. I don't feel like a human any more," he says.

A large proportion of failed asylum seekers have some kind of mental health problem, charities say, the result of the stress through which they are living. Haile probably needs some kind of medical help, but in his limbo status it is hard to access. "They live on paracetamol," Nibizi says. Last year, Haile broke an index finger but, alarmed by the questions he was asked when he went to casualty, left the hospital without getting it treated; the bone has mended but the finger no longer bends, and juts out at an awkward angle.

Mimi, 33 Ethiopia

The worldly possessions of one asylum seeker living rough in Birmingham. Photograph: Fabio De Paola

Sleeping on the streets, as Mimi puts it, is "not easy for ladies", so she has been sleeping on the floor of three Ethiopian families, two days here, two days there, for the last two months, since her asylum claim was refused. The families help her because they know she would otherwise be on the streets, but she can see she is a burden they cannot afford. Each morning she wakes up, dresses and gets ready to leave the house before she gets in the way, pausing at the doorway to see whether they will invite her to sleep another night.

"It's not easy living like this. It makes you go mad. It makes you want to kill yourself," she says.

She uses the £10 vouchers from the Red Cross to help contribute to the food supplies of the families that she visits; she has lost her own appetite, she says.

There are no night shelters that failed asylum seekers can go to in Birmingham (the Salvation Army hostel is not allowed to accept them), but the Red Cross has told her about a place in Coventry, 20 miles away, which offers emergency shelter to destitute migrants. She calls but there are only men staying at the centre, and the woman who runs the centre suggests it might be not be ideal for her. Mimi will continue sleeping on sofas.

The majority of destitute asylum seekers live in similar conditions, sharing rooms with other asylum seekers who are still receiving state support – housing and a basic weekly allowance – as their first asylum claim goes through. Because there are no accurate sources of data, it is impossible to know how many people are sleeping rough and how many on sofas.

"It is a hidden problem," says Penny Walker, who runs the night shelter in Coventry as part of a housing co-operative. "As a rule, they don't beg, they don't commit crime. These people try to remain invisible all day. They don't want to be loitering; they don't want anyone to see them and wonder whether they are about to rob them. There is this huge emptiness, huge uncertainty."

She regrets not being able to offer Mimi a space to sleep, but the living space at the housing co-operative she runs with fellow environmental and peace activists is already full. Between 14 and 16 destitute migrants arrive each night at 9pm, receive a hot meal and sleep together in one room, on camp beds lined up, side-by-side, about a foot between each bed. The atmosphere tonight is cheerful, but it isn't always. A few years ago, a failed asylum seeker gave up and hanged himself from a tree in the garden.

"They come here exhausted once they have run out of friends on whose floors they can sleep. Often they've been sleeping in friends' cars. They wouldn't come here unless they were desperate," says Walker.

"People think we should give asylum only to those who have a genuine need, not to those who have a so-called bogus claim," she says. "But what people don't understand is that the system is not fair. People don't flee their country unless they have a very good reason for doing so, and it is difficult to prove what happened to you unless you have scars from torture up your arms. The fact that you failed in your asylum claim does not mean that you are not a genuine asylum seeker."

Walker argues that their determination to remain in these conditions is a reflection of the seriousness of their difficulties at home.

"Who would choose this sort of life?" she asks. "Nobody."

Muhammad, 27 Somalia

Muhammad is unsmiling and guarded, very troubled by the 18 months he has been sleeping in Birmingham's parks. He came here in 2008, helped by an uncle who bought him a plane ticket to Heathrow, where he was immediately arrested. He claimed asylum, giving details of the murder of both his parents in 2006, shot dead by al-Shabab militants as they were minding their vegetable stall in the village market. The gunmen were raiding the stalls; when his parents tried to protect their stock of bananas and tomatoes, they were killed. His claim for asylum was refused 18 months ago. Shortly afterwards, he had to hand over the keys to the hostel where he was staying; that was the last time he had a shower or slept in a bed. He hopes to appeal against the decision but has not yet managed to put together a new case.

Everything he owns he carries in his backpack – one shirt, one sheet, one T-shirt, one pair of shorts, two heavy files of documents relating to his case, letters, photographs. He sleeps with his head on the bag to be sure it is never stolen. He doesn't have a sleeping bag, so he relies instead on old cardboard boxes as protection against the wind.

He speaks almost no English, but explains through the translator that he has learned to understand "Move" and "Back home" from the refuse collectors who sometimes find him still asleep by the hedge or at the edge of the outdoors baseball court, where he usually spends the night. Sometimes some west Africans sleep there too, but he can't speak to them, because they have no common language. He admits he has become very lonely. Another Somalian whom he met occasionally at the Red Cross recently disappeared, leaving his cardboard boxes behind. Muhammad wonders if he was taken to a detention centre but is not sure.

With his Morrison's vouchers he has bought a pot of Nutella (£1.21), a long baguette (60p) and a bottle of Highland Spring water (78p), because he has no access to a tap. He will cut the baguette into small sections and that way it should last for three days, when he will return and spend the second £5 voucher.

"My ambition is to live in peace. My ambition is to get peace. I would like to work and contribute to the community where I live, which I cannot do now. There is no peace in Somalia."

He is not optimistic that an appeal to the Home Office would succeed. "The last letter they sent me, they said I should go back to Somalia. I will be killed in Somalia."

All names have been changed.

• This article was amended on 16 June 2010. The word straitened was mis-spelt in the original. This has now been corrected.