Minkie gained a first class degree from Central St. Martin's College of Art before working as a photographer for four years. She went on to gain a masters degree in Film Direction from the Royal College of Art and began working in television as a director of documentaries such as the award-winning Lock Up Your Daughters before moving on to drama series.

Minkie has worked extensively on well known TV productions including episodes of Holby City (BBC), No Angels (Channel 4), Hustle (BBC), Doc Martin (ITV), Dalziel & Pascoe (BBC), Skins (Channel 4) and New Tricks (BBC). Most recently she has worked on the new ITV production Britannia High.