Ellie, 27, wore a wig to mimic Kate’s cropped look from 2001.
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She also wore a Ginsberg is God T-shirt by fashion designer Bella Freud — daughter of artist Lucian.
Ellie is in London shooting biopic Moss & Freud, telling of the friendship Kate and Lucian struck up when he painted a nude portrait of her.
The picture sold in 2005 for nearly £4million.
Stage and screen veteran Derek Jacobi, 85, plays Lucian in the film written and directed by Oscar-winning New Zealander James Lucas.
As well as the artwork, it will centre on how the sitting changed their lives.
The piece in question later went to sell at Christie’s auction house for £3.9million.
Kate, who is an executive producer on the biopic, had a leading role in choosing Ellie to play her.
The former Calvin Klein model previously told The Guardian: ““As this is such a personal story of mine, it has been essential that I be involved with James in all aspects as the project has developed.
“I am thrilled by the recent casting and excited that the film will begin shooting soon.
“I cannot wait to see it.”