Apply to a PhD program. In order to become a university lecturer in the UK, you first need to get into a PhD program. Most lecturing posts in good universities in academic subjects (including the arts, humanities, and sciences) require a PhD as a minimum requirement. To get into most PhD programs, you will need to fill out an application, write a cover letter, and supply a sample of your writing or research. In some cases you will also need to complete some sort of graduate school entrance testing, although this varies.
