Are there any circumstances in which an employer can insist on recruiting either a man or a woman?

Yes. Under para.1 of sch.9 to the Equality Act 2010, an employer can insist on recruiting either a man or woman if an occupational requirement applies. An occupational requirement will apply where, having regard to the nature or context of the work, the employer applying the requirement shows that being of a particular sex is an occupational requirement, and the application of that requirement is a proportionate means of achieving a legitimate aim. The Equality and Human Rights Commission, in the Employment statutory code of practice (PDF format, 1.09MB) (on the EHRC website) gives the example of a unisex gym relying on an occupational requirement to employ a changing room attendant of the same sex as the users of that room. There is also a very specific exception concerned with employment for the purposes of an organised religion. The burden of proving that the particular exception applies is on the employer. Other exceptions relate to national security, service in the armed forces and certain educational appointments.