Matilda Chaplin, the daughter of John Clarke Chaplin, a solicitor, was born in Honfleur in 1846. As a young woman she decided to become a doctor. She attended classes at the London School of Medicine for Women in 1867and passed the preliminary examination for the licence of the Society of Apothecaries just before the society closed its professional examinations to candidates who had not attended regular medical schools.
In 1869, Sophia Jex-Blake was trying to be admitted to medical classes at Edinburgh University. The university court refused consent for mixed classes and was not prepared to make special arrangements for Jex-Blake alone, but conceded that special classes for a group of women might be possible. Jex-Blake advertised for women to join her and Matilda Chaplin was one of those who accepted her invitation. In October 1869 Chaplin, together with four other women, passed the matriculation examination for Edinburgh University, the first women to be fully enrolled at a modern British university.
In 1870–71 Chaplin took high honours in anatomy and surgery at the extramural examinations of the Royal College of Physicians and Surgeons of Edinburgh. In 1871 attended some medical classes in Paris. She was also involved in the struggle for women's suffrage and was a member of the London National Society for Women's Suffrage.
On 21st December, 1873 she married her cousin, Professor William Ayrton. The couple moved to Japan as her husband had just been appointed professor of physics and telegraphy at the new Imperial Engineering College in Tokyo. Matilda started a school for Japanese midwives while living in the country. She also continued with private medical studies and wrote and illustrated several newspaper articles about her travels. A daughter, Edith Ayrton, was born in 1879.
Matilda Ayrton continued with her studies and after obtaining a MD in Paris she became a licentiate of the King and Queen's College of Physicians in Ireland in 1880. She then began practice in Sloane Street, while studying diseases of the eye at the Royal Free Hospital.