Georgiadis was born in 1939 in Southend-on-Sea, east of London. He took up the violin at six, studied at the Royal Academy of Music, and immediately began to land top chairs in the violin sections of British orchestras. He was leader of the City of Birmingham Symphony Orchestra for two years, and then, in two stretches between 1965 and 1979, served as leader of the London Symphony. That was during a period of golden years for the orchestra, and Georgiadis can be heard on many classic recordings featuring conductor John Barbirolli. He recorded the violin concerto of Ernest John Moeran with the LSO in 1977. Georgiadis has made more than 250 appearances as a violin soloist and also spent four years (1986-1990) as first violinist of the Gabrieli String Quartet.
Georgiadis' career as a conductor began in the mid-1970s with appearances leading the Liverpool Philharmonic. He studied for eight years with conductor Sergiu Celibidache and then undertook a long series of guest conducting appearances with many British orchestras. Georgiadis' music directorships have included those with the London Virtuosi, the Essex Youth Orchestra, the Bristol Sinfonia, and, from 1994 to 1996, the Bangkok Symphony, which he built from a part-time group into a world-class ensemble. Georgiadis has also guest conducted the Malaysian Philharmonic Orchestra. He was active as a music educator, serving as Director of Orchestral Studies at the Royal Academy of Music.
Georgiadis was hardly slowed by senior citizenhood, releasing more albums after reaching the age of 65 than he had previously. Many of these recordings are devoted to the music of Johann Strauss II and his contemporaries, a repertory he championed, bringing him honorary membership in the Johann Strauss Society of Great Britain. On these recordings, he led the Czech Chamber Orchestra Pardubice, and with that group he released Contemporaries of the Strauss Family, Vol. 4, on the Marco Polo label in 2019, at the age of 80.