In the late 1950's, a new subculture appeared in British youth culture, mainly in London. For the first time, teenagers had money, because they didn't need to contribute to the family with their after-school jobs. They spent it on records (modern jazz, ska, reggae, R&B, soul, British bands such as The Who, The Small Faces etc.) and on clothes (Carnaby street fashion, mainly tailored but later, brands such as Fred Perry and Ben Sherman). They drove Vespa and Lambretta scooters.
Wear Fred Perry shirts, button-down shirts (merc, Ben Sherman), sta press trousers and slim-fit suits. For shoes, try desert boots, pointy shoes or groovy trainers like Adidas Samba.
If you are a female, wear short bright colored frocks and tall bright boots. Also light makeup and minimal wings on eyes a must. Make your eyes stand out with white eyeliner on the bottom of your eyes.
Refrain from buying yourself a leather jacket, unless you want to be a rocker.