Are there any circumstances in which an employer can specify, for example, the required race, gender, sexual orientation or age of job applicants?
Yes, there are certain defined exceptions in the Equality Act 2010, known as occupational requirements. These, broadly, apply when a job can be performed effectively only by someone with a particular protected characteristic, eg either a man or a woman, a person of a specific racial or religious group, a person of a particular sexual orientation, a disabled person or a person of a particular age group.
To rely on the exception, the employer must show that, having regard to the nature or context of the work, having the particular protected characteristic is an occupational requirement and that the application of the requirement is a proportionate means of achieving a legitimate aim.
For example, the Equality and Human Rights Commission, in the Employment statutory code of practice, states that "a women's refuge which lawfully provides services to women only can apply a requirement for all members of its staff to be women".