Hawes, 37, had been sharing the stage with Sheila Hancock in the critically acclaimed stage comedy at Wyndham's Theatre since September.
However, Hawes abruptly left the production last week because she and Hancock have not been getting along, the newspaper said, citing an unnamed source as reporting there was a "battle between two divas."
"Sheila has forthright views about how performers should act in the play. She has a reputation for being blunt," the insider said.
The Independent said neither Hawes nor Hancock could be reached for comment regarding its story.
Hawes' understudy will replace her until the production wraps Saturday.