Moving in a Vulnerable Friend
This situation is difficult enough when both friends are functioning, healthy people, but when you throw in a dynamic such as serious mental illness, drugs or alcohol abuse issues, a whole different class of problems can arise.
I'm not for one minute suggesting that everyone who suffers from mental illness or has drug or alcohol issues isn't capable of leading a normal life, but I am saying that while your friend is in crisis it may not be realistic to expect to be paid any money, even your expenses, from such an arrangement, or expect your "lodger" to adhere to any house rules (however reasonable and commonplace!).
If your friend has serious problems, such as mental health issues or drug dependency - you would be advised not to offer your room unless you know the person really well OR you've had plenty of experience of helping people through these particular problems and you're prepared to be more carer than flatmate. In short, you need to know exactly what you're doing, and be prepared for the day to day reality of the situation. Otherwise, you must accept that your friend needs specialised help, and the best way you can help them is by supporting them in finding appropriate housing.
A good start is to put them in touch with organisations that can help to house vulnerable people, but first encourage them to ask their family doctor (and/or their social worker, key-worker or support worker if they have one) to support them to be assisted by the housing authority as a vulnerable person with a priority need for housing. Please see the Crisis website for separate definitions of the term "vulnerable person" in England and Wales as it applies to housing - note that although English and Welsh local authorities have a legal duty to house the vulnerable homeless, each local authority has broad discretionary powers on deciding who is "vulnerable". Scottish local authorities now have a duty to house anyone who becomes homeless through no fault of their own, following the Homelessness (Abolition of Priority Need Test) (Scotland) Order 2012.
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With an acute shortage of public housing, the single able bodied (or at least, those who appear able bodied on the surface) under 60 who don't have children living with them are very unlikely to be offered any accommodation in certain areas. In other areas, they may have wait it out in temporary housing for months or even years, even if they meet the other priority need criteria.
If your friend is over 55 they may have some eligibility for sheltered housing schemes for the elderly - more likely with housing associations rather than local authorities.
Unlike Scotland, English and Welsh Local authorities are not legally obliged to put single people on the public housing waiting list, but they can still offer temporary accommodation or may refer your friend to local schemes that place homeless people in private rented accommodation and assist with the required deposit. By law, they must at the least offer advice. Even in Scotland, however, local authorities can only priotise those in need and offer public housing when and where available.
There are many families with young children who can't get social housing in many built up areas. In fact the housing situation in such areas is so critical that local authorities as a rule will not even house families in temporary accommodation until bailiffs literally evict them from private accommodation.
Unfortunately, particularly during this time of austerity with a worse than ever housing crisis, your friend may have to fight hard simply to be recognised as being in priority need, let alone offered any form of help - someone who is already feeling very low is going to find this especially difficult - you can help by attending appointments with your friend and putting their case for them. Be sure to do your research thoroughly first so you know what help your friend is entitled to inside out, as there have been plenty of cases where single homeless people have been misinformed by local authorities of their rights and what help is available to them in the area!
If your (UK based) friend is homeless, or facing homelessness (has been given notice to move out of their present accommodation in England or Wales within 28 days or within 2 months for Scotland) for England and Wales, visit Shelter England, before your friend contacts the local authority Homeless Persons Unit or Shelter Scotland for Scotland.
The Mind website is another helpful source of information on UK housing options for people with mental health issues.