Unlawful Discrimination
There are legal obligations on landlords and agents to take reasonable steps to ensure that people are not discriminated against directly or indirectly due to their "protected characteristics" such as race, colour, gender or disability. The specific legislation is the Equalities Act 2010.
Direct discrimination is defined as treating a person less favourably than another based on their race, gender or disability. In some cases, discrimination may occur where there has been a failure to comply with a statutory duty. Regarding disability, you should note that the statutory definition has been widened to include those with certain long-term medical conditions.
Indirect discrimination consists of applying a requirement or condition that, although applied equally to persons, whether male or female, black or white, is such that a considerably smaller proportion of a particular racial or gender group can comply with it than others, and it cannot be shown to be 'justifiable'.
Concerning issues pertaining to disability, a similar requirement exists that landlords do not impose criteria that could be identified as 'unreasonable'.
The Equality and Human Rights Commission published a code of practice on racial equality in housing. The code is essential because it is a statutory code, which Parliament has approved. The courts will consider the code's recommendations in legal cases. The code is in two main parts; the first explains what landlords need to know about discrimination; the second makes recommendations about how landlords can avoid being discriminatory.
See here to find out more about discrimination and guidance on avoiding discrimination.
The landlord should note that they must not choose contract-holders based on race, religion, marital status, disability or sexuality. If the landlord discriminates against any tenant on these grounds, the landlord could be prosecuted. If the landlord is letting rooms in the landlord's home, the landlord may specify the sex of prospective lodgers. Age discrimination is prohibited in employment but is allowed in housing. In some cases, housing might have to be let to those over 55 to comply with planning requirements.
No DSS adverts
Several cases have found unlawful landlords or agents who operate blanket "no DSS" policies or advertise their properties as "no DSS" or similar.
See, for example, this report and another here.