In a recruitment or promotion situation, is an employer obliged to offer the position in question to a candidate with a protected characteristic that is under-represented?

No. A position for recruitment or promotion should always be offered to the best candidate. An employer that offers a position to a less suitable candidate just because they have a targeted protected characteristic risks being guilty of unlawful positive discrimination. The positive action provisions in s.159 of the Equality Act 2010 provide very limited scope for employers to apply positive action to select a candidate with an under-represented protective characteristic, where candidates are equally qualified. In reality, situations in which an employer has two candidates for recruitment or promotion, but with genuinely no preference between them, will be rare. It is only where the employer could, effectively, make its selection by tossing a coin that the candidates could truly said to be of equal merit.