Advisers at Shelter's national helpline are doing everything they can to make the call-centre office feel like a cheerful environment. Tinsel with Christmas baubles has been hung from the ceiling, tiny silver Christmas trees and felt reindeer have been stuck on the tops of computer screens, cotton-wool icicles are hanging from the windows, and colleagues have brought in mince pies and chocolates to share.

You quickly understand why maintaining a good mood in the office is important if you spend time listening in to the calls that come in, at a rate of around 500 a day, from people facing imminent homelessness or already sleeping rough and seeking advice about how to find somewhere new to live.

The anxiety and emotion that pours into the headsets of crisis advice workers in this crowded fifth-floor Sheffield call centre offers a snapshot of the UK's worsening homelessness crisis. Advisers at Shelter's helpline are processing more calls than ever. Last year there was a 15% increase in the volume of calls – a reflection, staff think, of the degree to which people are struggling with rising house prices, soaring rents, cuts to housing benefit and the long shadow of the recession. A day spent at the centre provides a clear picture of the kinds of housing problems people face, as pressure on council house stock intensifies and radical changes to benefit entitlements are introduced.

An employment adviser calls on behalf of a 23-year-old client whom he is trying to help find work – a process that is complicated by the fact that the man, and his young girlfriend, have nowhere to live and are sleeping on the streets. The girlfriend is 18 weeks pregnant and, for reasons that are unclear, her father has thrown her out. Sharon Reeves, one of the helpline advisers, calmly explains the best course of action. "If she is pregnant, they would be in priority need. It sounds like the council has just fobbed them off. They should have provided them with a bed and breakfast to stay in. They should really go back to the council and challenge it," she tells the man.

"He's been three times already. I told him not to leave this time until he gets a B&B or a hostel. Anything is better than being on the streets," the employment adviser replies, audibly distressed by the situation faced by the couple. Reeves is touched that the employment adviser has been dismayed enough by his client's situation to want to try to help. "Some people are still shocked, but it doesn't surprise me – I hear it a lot," she says. She has been working in the call centre for five months and is already familiar with similar situations. "All the calls are awful when you first start. Now it already feels commonplace."

She appreciates that council staff in housing departments are under increased pressure. "It's not easy for the council; they haven't got any housing stock, but they just need to find them a B&B for the meantime," she says. She moves quickly to her next call, which comes from a man who has recently come out of prison and is alternating between sleeping on the floor of his sister's home and sleeping on the streets.

Another adviser takes a call from a young woman from London explaining that she has been forced to flee her home because of domestic violence, that she moved temporarily to a women's refuge, which didn't work out. She subsequently moved with her nine-year-old daughter to sleeping on the sofa of her mum's house, but has been kicked out. When she visited the council, the housing officer suggested that she return to her marital home as some time had elapsed (five months) since her husband was violent towards her. "The woman was really horrible to me. She looked at me like dirt," she says.

"She shouldn't have said that. It's unlawful," the Shelter adviser explains. "If you have been the victim of domestic violence, you shouldn't be asked to go back there."

"I don't care where I go. They can put me in a dirty, disgusting room somewhere." The adviser promises to get her some legal aid-funded advice.

The phone calls come through relentlessly, and advisers have barely a minute to write notes on each call before they have to move on to the next one. A woman with a 20-month-old son rings in, her voice wobbling with the strain as she tries to explain her situation over the noise of a baby intermittently crying and gurgling. She has been asked to leave the flat she is renting by 4 January; she thinks the landlord's decision is probably connected to the fact that her child's father has neglected to pay the rent since he walked out on them. The landlord is so annoyed at the arrears that she has refused to deal with a boiler problem, and they have had no hot water for three weeks. An adviser gives clear advice on what her rights are, and explains where she can go to get more support.

Another woman in a similar situation calls to say that bailiffs are due because her ex-partner stopped paying the mortgage when he left her and their eight-year-old son three months ago. "I don't want to be evicted until we find somewhere else to live," she says, anxiety cracking her voice. "If I don't resolve this issue, my daughter and I are going to be homeless."

Helpline adviser Nadeem Khan counsels a woman, who is holding a noisy baby close to the phone, on how to extract herself from a joint tenancy with her husband, who has also walked out on her and who, it has subsequently emerged, had in any case not been paying the rent previously, so has left her saddled with huge rent arrears, which she is not able to pay, and which may trigger her eviction.

Official homelessness figures released in early December showed that 2,100 homeless families in England were living in emergency bed and breakfast accommodation – the highest number in a decade. The total number of families living in all forms of temporary accommodation rose by 5% on the previous year. There was a sharp increase in the number of people formally accepted as homeless in London.

A quarter of calls come from London, a reflection of the extreme prices in the capital. "If you are an ordinary person in London, you don't even need to have a particular problem to find housing difficult – you just have to be looking for somewhere to live," says Liz Clare, team leader at the helpline.

The Shelter housing advice helpline is staffed 365 days a year. "Sadly the continued pressure of soaring living costs, combined with cuts to the housing safety net, means that many will face an ongoing struggle to stay in their homes," says Campbell Robb, Shelter's chief executive. Another adviser, Anna Newton, says after four years working here, she can judge the level of distress instantly by the caller's voice. "More often than not people are very upset; we hear from a lot of single mothers who have got into financial difficulties and are being evicted for rent arrears. Sometimes people don't realise the seriousness of the situation they are in, they think there must be some safety net, and sometimes there just isn't any," she says. "The calls are often very harrowing."

This year she has found it more challenging to direct people towards experts outside the charity, partly because of legal aid reductions. "Legal aid is much more limited – there is no longer legal aid for benefit claims. We signpost the Citizens Advice, but they are oversubscribed too," she says.

A woman calls on behalf of a friend who is HIV-positive and homeless, to establish whether his medical condition is likely to make him eligible for extra support. The adviser explains that the man must be prepared to make a persuasive and powerful case to the council housing officers. "He needs to show the council that his condition makes him more vulnerable if he becomes street homeless. He needs to say: 'I am HIV positive and I am very unwell and I have nowhere to live.' He needs to make that very clear to the council. They should give him emergency housing, but many councils these days throw a lot of difficulties in the way," the adviser says.

'More often than not people are very upset … The calls are often very harrowing.' Photograph: Christopher Thomond for the Guardian

A man from Spain, who has been working in Britain for two years, calls to say that he needs to find somewhere to live because his wife and two young children are coming to join him next week, and although he has money to pay rent, no estate agent or landlord will deal with him because he has been working on zero-hours contracts and is not viewed as a dependable tenant. The council has told him there is nothing it can do to help him.

Someone else rings because a landlord promised to deal with mould on the bedroom walls and holes in the kitchen floor before they moved in, but the landlord has only put a slap of paint on top of the mould, and now the rent has been paid, but the flat is uninhabitable.

Changes to housing benefit payments appear to be part of the reason why one woman and her five children are facing eviction. She cannot understand why she is in arrears as she was under the impression that her rent was being paid in full by the housing benefit department, and no one has been able to tell her how much her arrears amount to. She has started paying the money back at £130 a month, but this appears not to have been enough to stall the eviction process.

"If I lose the house, social services say the children are going to be taken into care. I have rung the agents numerous times. I've asked them to send a statement of what is outstanding," she says. "My rent goes straight to the agency so I didn't know what was being paid. I didn't know they weren't paying the rest until I had the possession order. I would have paid what I have to pay if I'd known I had to pay anything."

The Shelter adviser is sympathetic. "It may not have been clear to you exactly what you have to pay. There may have been a deduction in the rate and you may not have been aware of that," he says.

Liz Clare says the work is becoming increasingly difficult. "It is clear from working the helplines that pretty much anyone can have a housing problem. You can go from being comfortably housed to being on the brink of eviction, just by losing a job or getting ill," she says. "There is a shortage of housing and it is very, very expensive. People's salaries are not going up. People are really, really struggling. It has become more difficult to get help because of changes to legal aid. People are often very tearful – it can be very upsetting to hear the emotion coming down the line. Often just having someone on the phone being nice to them can set them off."

The work can be distressing for advisers. "You have calls from people on the brink of eviction, who really want to turn their circumstances around, but who don't have the resources. For single people who have fallen on hard times, there is not much help. There isn't any duty from the local council to house them. It is hard in London even to get space in a hostel. You may have to say to them 'Unfortunately tonight you don't have any option but to stay outside.' That can be very upsetting. People often don't understand that it is the only option."

A woman calls to try to understand whether she can help an acquaintance from South America, who has lived here for 10 years, and who has become homeless with her nine-year-old child. The two women attend the same church and the caller wonders if she can let her stay in her family home, or whether that is likely to worsen her longer-term chances of being housed by the local council.

"She is living in wildly unsuitable accommodation. They are staying in a one-bedroom flat, with a woman who has mental health issues, a long way from the girl's school. The lady they are staying with desperately wants them to leave. It is a ridiculously unsuitable place for them."

It is a complicated situation, which requires the adviser, Nadeem Khan, to consult colleagues at length, but his advice is clear – that the caller can give her a room, and that the woman is entitled to better help from the council. Her thanks is heartfelt at the end of the call. "That has probably been one of the most useful phone calls I have ever had," she says.

Contact Shelter's free housing advice helpline on 0808 800 4444 (calls are free from UK landlines and main mobile networks), or go to shelter.org.uk