Discrimination was addresses by the Equalities Act 2010
This Act consolidated all previous discrimination Acts.
Illegal on the grounds of race, religion, colour, ethnicity, sex or disability.
Agents and landlords may be obliged to carry out reasonable adjustments for disabled tenants e.g. grab handles. Landlords are not normally obliged to make major alterations to assist the disabled although many do.
Note that age discrimination is only prohibited by employers.
When letting – a group of 20 year old girls seeking a house mate are entitled to exclude anyone based on any age, sex, or e.g. personality. This is logical, otherwise tenants would be unable to choose their house mates. Letting agents would be unable to reject unsuitable prospective tenants.