The Sunday Telegraph's theatre critic, Tim Walker, said she never needed to ride on the coat-tails of her famous relations.
He said Richardson took the decision early in her career to "stand or fall on her own" and left London to begin her career in Leeds at the West Yorkshire Playhouse.
"The world of acting has been deprived of a great actress, really in her prime," he said.
"She had a sort of luminous presence on the stage, but off-stage she was a very shy, easy-going, almost self-deprecating character who didn't like being made a fuss of."
Richardson, whose father director Tony died of Aids-related causes in 1991, was on the board of the US-based charity amfAR, The Foundation for Aids Research.
A spokeswoman for the charity said she was a "dedicated Aids advocate" and an "eloquent spokesperson for amfAR".
"Our hearts go out to her family. This is a catastrophic loss for them, and it is a terrible loss for amfAR and the fight against Aids," she said.
"She generously contributed her time and resources to amfAR for over 15 years."
It is not known exactly what happened to Richardson.
However, leading neurosurgeon Chris Chandler said a seemingly minor blow on the head can cause life-threatening injuries.
Mr Chandler, from King's College Hospital in south London, said the effects of a blow to the head may not become apparent until several hours afterwards and, if untreated, a patient can fall into a coma.
"A blow to the head can cause a bruise or rupture a blood vessel that slowly swells, causing pressure to build up inside the skull," he said.
"In the skull there is nowhere for the brain to move to so pressure continues to grow and that swelling can cause the brain to malfunction because it can limit circulation.
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