The correspondence was penned in 1873 by Sophia Jex-Blake, a campaigner for female admittance to British universities who eventually became the third registered woman doctor in the country.
Lis Smith said she was “astounded” to uncover the letter in the university archives.
“We knew that Sophia Jex-Blake and her supporters, in their quest to open up university medical education for women, had written to the Senatus Academicus at St Andrews in an attempt to gain admittance to classes there, but we didn’t know documentary evidence existed,” she explained.
“While searching the archives for information about the university’s higher certificate for women, I was astounded to come across what must be the very letter Jex-Blake wrote.”
The letter was signed by Ms Jex-Blake and ten other campaigners for female admittance to university. Several were also fighting for female suffrage.
They offered to build or hire new premises and arrange lectures in subjects that were not already part of the St Andrews course.
However, the request was unsuccessful and it would not be until 1892 that women were admitted as full students to St Andrews.
In 1874 Ms Jex-Blake helped set up the London School of Medicine for Women.
Three years later she became the third female doctor in the country to register with the General Medical Council after obtaining an MD at the University of Berne.
Ms Smith said most of the signatories of the 1873 letter did eventually succeed in practising as doctors by qualifying outside the United Kingdom while Jex-Blake herself went on to set up the Edinburgh School of Medicine for Women in 1886.