She has received 12 nominations for the Academy Award for Best Costume Design and has won three times for A Room with a View (1985), Mad Max: Fury Road (2015), and Cruella (2021).

She has also been nominated for the BAFTA Award for Best Costume Design ten times and had a record four wins for A Room With a View, Gosford Park (2001), Mad Max: Fury Road, and Cruella.

On television, Beavan has been nominated for the Primetime Emmy Award for Outstanding Costumes for a Miniseries, Movie, or Special five times, winning twice for Emma (1996) and Return to Cranford (2010).

She has frequently worked with costume designer John Bright, who runs the costume-rental house Cosprop, and credits him with educating her as she was starting out her career.

[4] In 2016, Beavan won her 3rd BAFTA and 2nd Academy Award in George Miller's post-apocalyptic action film Mad Max: Fury Road.

[8][9] In June 2018, Beavan was awarded an Honorary Fellowship by Arts University Bournemouth alongside dancer Darcey Bussell, graphic designer Margaret Calvert, OBE, and director and screenwriter Edgar Wright.