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.
A landmark court case ended with a landlord and their letting agent paying £4,500 for refusing to show a property to a potential tenant because they were claiming benefits.
This page looks at the Equality Act 2010. In particular, the most common duty under the Act for landlords will be adapting premises for disabled persons.