It is not possible to give an exact year when the Catholic Church began to be called the "Roman Catholic Church," but it is possible to approximate it. The term originates as an insult created by Anglicans who wished to refer to themselves as Catholic. They thus coined the term "Roman Catholic" to distinguish those in union with Rome from themselves and to create a sense in which they could refer to themselves as Catholics (by attempting to deprive actual Catholics to the right to the term).
Different variants of the "Roman" insult appeared at different times. The earliest form was the noun "Romanist" (one belonging to the Catholic Church), which appeared in England about 1515-1525. The next to develop was the adjective "Romish" (similar to something done or believed in the Catholic Church), which appeared around 1525-1535. Next came the noun "Roman Catholic" (one belonging to the Catholic Church), which was coined around 1595-1605. Shortly thereafter came the verb "to Romanize" (to make someone a Catholic or to become a Catholic), which appeared around 1600-10. Between 1665 and 1675 we got the noun "Romanism" (the system of Catholic beliefs and practices), and finally we got a latecomer term about 1815-1825, the noun "Roman Catholicism," a synonym for the earlier "Romanism."
A similar complex of insults arose around "pope." About 1515-25 the Anglicans coined the term "papist" and later its derivative "papism." A quick follow-up, in 1520-1530, was the adjective "popish." Next came "popery" (1525-1535), then "papistry" (1540-1550), with its later derivatives, "papistical" and "papistic." (Source: Random House Webster's College Dictionary, 1995 ed.)
This complex of insults is revealing as it shows the depths of animosity English Protestants had toward the Church. No other religious body (perhaps no other group at all, even national or racial) has such a complex of insults against it woven into the English language as does the Catholic Church. Even today many Protestants who have no idea what the origin of the term is cannot bring themselves to say "Catholic" without qualifying it or replacing it with an insult.