The show, which was watched by 4.3 million viewers, according to unofficial overnight figures, featured Barrett working in the kitchen of Ozer, a Turkish restaurant in Oxford Circus, where she prepared a dish of venison with aubergine caviar, which received positive feedback from judges John Torrode and Greg Wallace.
The final round of the competition saw the competitors preparing their best two meals.
Barrett decided to cook char-grilled duck breast with an Asian-style green salad and pomegranate seeds for her first dish, and pan-fried sea bass with saffron mash and lemongrass beurre blanc for her second, which took her through to the MasterChef quarter-final.
Barrett said: "Now I'm through to the quarter-final, the pressure is on. I just hope I can go all the way."
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