Moran was born in Brighton, attended a Methodist primary school in Wolverhampton, and was then educated at home from the age of 11. At the age of 15 in 1990, she won The Observer's Young Reporter of the Year. She began her career as a journalist for Melody Maker, the weekly music publication, at the age of 16. Moran also wrote a novel called The Chronicles of Narmo at the age of 16, about being born into a family of eight home-educated children in Wolverhampton.

In 1992 she launched her UK television career, hosting the Channel 4 music show "Naked City", which ran for two series and featured a number of then up-and-coming British bands such as Blur, Manic Street Preachers, and the Boo Radleys.

In December 1999, Moran married The Times rock critic Peter Paphides in Coventry and the couple have two daughters; Dora (b. February 2001) and Eavie (b. August 2003).