A number of privately owned telegraph companies operated in Britain from 1846 onwards. In 1868 these all came under the control of the newly formed GPO (General Post Office). With the invention of the telephone in 1876 the GPO began to provide telephone services from some of its telegraph exchanges. In 1969 the GPO, a government department, became the Post Office. Telecommunications was split off, as British Telecom, in 1981.
2022: Londonist have posted a very useful page on phone boxes.