Costa is a former member of the British boyband Blue. He attended Hendon School in North-West London. He is Greek Cypriot on his father's side and Jewish on his mother's; he has as a sister Natalie and brother Louis.

In 2004 Costa, along with singer Peter Andre, were given the opportunity to meet with Prime Minister Tony Blair at the celebrations on the arrival of ten new members into the European Union which also included Cyprus. He was a contestant on the 2005 series of I'm a Celebrity, Get Me Out of Here! and was evicted from the programme on the 3 December 2005 after 14 days.

Costa released his first solo single called "Do You Ever Think Of Me" in February 2006. The single made its debut at #19 on the UK Singles chart. He went on to compete in the 2006 "Making Your Mind Up" programme to find a competitor to represent the UK in the 2006 Eurovision Song Contest, but did not win the 'honour'.

Since 10 April 2006, Antony has been playing the lead role on Mickey Johnstone in the London production of the long-running musical Blood Brothers, directed and produced by Bill Kenwright. His contract runs through to the summer.

Albums 2006 - Heartful of Soul - Not Yet Released.