In 1996, he successfully auditioned for the role of Martin Fowler in EastEnders. The character had actually been created shortly after the show's inception in 1985, but the role had become vacant following the departure of the previous actor Jon Peyton Price.
Alexandrou appeared in the short film Blessed Burden. In 2003, he won a celebrity edition of The Weakest Link.
On 14 April 2006, it was announced that Alexandrou wished to leave EastEnders in autumn 2007. He and Natalie Cassidy, who played his on-screen wife Sonia Fowler, left on 2 February 2007 (to tie in with the exits of Wendy Richard and Ray Brooks); although the door has been left open for a possible return in the future. He said "I've decided to leave the show to experience other aspects of my industry. Having turned 21, I felt it was a good time to leave. I owe everything to the show and would love to come back one day - that's if EastEnders would have me."