Lesley, who made medical history on July 25 1978, when she gave birth to her daughter Louise, died from septicemia on June 6 after being admitted to hospital with gallstones.
She and her husband John had been trying for a baby for nine years when they were referred for potential In-Vitro Fertilisation (IVF) treatment, when eggs are fertilised with sperm outside the body and implanted into the womb. Lesley's blocked fallopian tubes meant getting pregnant naturally was impossible for her.
Lesley, from Bristol, agreed to the experimental procedure, pioneered by Professor Bob Edwards and Dr Patrick Steptoe in Cambridge. Amazingly, the ground-breaking technique worked the first time for the couple - and their lives were changed forever.
They also needed only one cycle to conceive their second daughter, Natalie, four years later. Although Dr Steptoe died in 1988, Louise remains close to Professor Edwards.
Since then more than three million babies have been born worldwide using the same technique.
Lesley died at the Bristol Royal Infirmary following a short illness and leaves step-daughter Sharon and daughters Louise and Natalie and five grandchildren. Her husband, John, passed away five years ago.
Her daughter Louise said:
Mum was a very quiet and private person who ended up in the world spotlight because she wanted a family so much. We are all missing her terribly.
Speaking on behalf of Professor Edwards and the team at Bourn Hall Clinic, Mike Macamee, CEO, said: "Lesley was a devoted mum and grandmother and through her bravery and determination many millions of women have been given the chance to become mothers. She was a lovely gentle lady and we will all remember her with deep affection."
Speaking in 2008 Mrs Brown said she had felt so desperate to have a baby, she was willing to put up with anything to give birth.
Although other women had been implanted with fertilised eggs, Mrs Brown was the first to achieve a pregnancy which went beyond a few weeks.
Nevertheless, there were some who feared the baby would be abnormal and it was only after Louise's birth on July 25, 1978, that minds could be put at rest.
Annoucing Louise's headline-making birth, Dr Steptoe said: "All examinations showed that the baby is quite normal."