On 25 December 1952, Queen Elizabeth II made her first Christmas broadcast to the nation as sovereign on BBC radio. The tradition of the Christmas broadcast began in 1932 with the Queen’s grandfather, King George V. In 1952, at 15.07 p.m. the Queen broadcast from the study at Sandringham House, Norfolk. Families around Britain would listen to the Queen huddled around their radios, for some it became essential Christmas listening.

The Queen’s speech was heard in the many Commonwealth nations who held her as head of state over the following days. She referenced her family Christmas and sent her ‘affectionate greetings’ to those in the armed forces serving abroad ‘in snow or sunshine’. Her Majesty also thanked the public for their support for her as monarch in the ten months since her father, King George VI, had died on 6 February 1952 and requested peoples’ prayers for her coronation the following year. 

The Queen’s speech was first televised in 1957 and from 1960 the television and radio broadcasts were pre-recorded in the run up to Christmas. 

https://www.youtube.com/watch?v=2nTaiHXvVI0

Source:

http://news.bbc.co.uk/onthisday/hi/dates/stories/december/25/newsid_3053000/3053271.stm