Ms Lister was paralysed from the neck down and used the “sip-and-puff” system for steering and controlling the sails of her yacht.
She was the first quadriplegic to sail across the English Channel in 2005.
She then became the first female quadriplegic to sail around the Isle of Wight in 2007 and went on to sail solo around Britain in 2009.
The International Sailing Federation (ISAF) decided that the achievement put her in the top four sailors in the world.
An announcement of her death was published on her website, which called her “an inspiration to many, a recipient of many accolades and a record holder of many sailing achievements”.
Paying tribute to his stepmother, Alex Lister said: “She turned the suffering she was experiencing into an opportunity.”
Ms Lister was born able-bodied but had a degenerative condition reflex sympathetic dystrophy, and had to use a wheelchair from the age of 15.
She studied biochemistry at Jesus College, Oxford, but while there her condition deteriorated and she became paralysed from the neck down at the age of 27.
Ms Lister, of Canterbury, Kent, began sailing with Westbere Sailing Opportunities in Canterbury in 2003, and said: “Within 30 seconds of being in a boat I was in love.”
The Sunday Times named her Sportswoman of the Year 2007 and she won a string of other accolades, including a Cosmopolitan Superhero Award and the Royal Cruising Club’s Seamanship Award 2005.
Hilary’s Dream Trust, her charity, supports disabled and disadvantaged people taking up training.