The traditional English pronunciation of Latin, and Classical Greek words borrowed through Latin, is the way the Latin language was traditionally pronounced by speakers of English until the early 20th century.
In the Middle Ages speakers of English, from Middle English onward, pronounced Latin not as the ancient Romans did, but in the way that had developed among speakers of French. This traditional pronunciation then became closely linked to the pronunciation of English, and as the pronunciation of English changed with time, the English pronunciation of Latin changed as well.
Until the beginning of the 19th century all English speakers used this pronunciation, including Roman Catholics for liturgical purposes. Following Catholic emancipation in Britain in 1829 and the subsequent Oxford Movement, newly converted Catholics preferred the Italianate pronunciation which became the norm for the Catholic liturgy. Meanwhile, scholarly proposals were made for a reconstructed Classical pronunciation, close to the pronunciation used in the late Roman Republic and early Empire, and with a more transparent relationship between spelling and pronunciation.
One immediately audible difference between the pronunciations was in the treatment of stressed vowels, in which the English version followed the sound changes that had affected English itself, the stressed vowels being quite different from their unstressed counterparts, whereas in the other two versions they remained the same. Among the consonants, treatment of the letter c followed by a front vowel was an obvious distinction. Thus the name Cicero was spoken in the English version as Sisero, in the Italianate as Chichero and in the restored classical as Kikero. (Similarly with et cetera, etc.)
The competition between the three pronunciations grew towards the end of the 19th century. By the beginning of the 20th century, however, a consensus for change had developed. The Classical Association, shortly after its foundation in 1903, put forward a detailed proposal for a reconstructed classical pronunciation. This was supported by other professional and learned bodies. Finally in February 1907 their proposal was officially recommended by the Board of Education for use in schools throughout the UK. Adoption of the "new pronunciation" was a long drawn out process, but by the mid-20th century, classroom use of the traditional pronunciation had ceased.