If the employer has refused you a job because of your physical appearance, the organisation may be engaging in unlawful discrimination. Discrimination will be no less unlawful just because it is subconscious or unspoken, or because it is based on ingrained or stereotypical assumptions. The employer may not even be aware that they are engaging in discrimination.
It would, for example, be unlawful to discriminate against you because you don’t fit the 'image' of the employer – because you are considered 'too old' for their target market or because you have a disfigurement (which would be disability discrimination).
There are rare exceptions of professions, such as modelling or acting, where an employer is still likely to discriminate openly and lawfully on grounds of physical appearance. This is known in law as a 'genuine occupational requirement'.
The law does not stop an employer setting minimum criteria about appearance, such as wanting someone to be smartly dressed or presentable, and recruiting on this basis.
It is not unlawful sex discrimination for an employer to have a dress code with different requirements for each gender – such as a tie for men and smart clothes for women – as long as an equal level of smartness is expected of both sexes.
Dress codes must not be sexist. Unions campaign for the abolition of sexist dress codes that require women to wear inappropriate clothing, high heels and make up. Join a union if you would like to see an end to these sorts of practices where you work.