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I found this quote at Quora:
In March 1916 Ramanujan graduated from Cambridge with a Bachelor of Science by Research (This degree was later renamed as Ph.D. from 1920) for his work on Highly composite numbers.
Given how important his paper on Highly composite numbers was it appears that Cambridge upgraded their policy specifically for him; but I'm unable to find anything more on the internet about this.
It does not appear that Cambridge changed the policy for Ramanujan, although they did use a rather atypical degree they had for him (Bachelor of Arts by Research, not Bachelor of Science by Research). PhD in Mathematics was not traditional in Britain, and was only created after the First World War. Ramanujan was a beneficiary of the general conversion in 1920s. Here is from The Mathematics PhD in the United Kingdom: Historical Notes for the Mathematics Genealogy Project:
"The UK has an unbroken tradition of 800 years of university mathematics but for nearly all of that time the creation of doctors played no part in the process of preparing the next generation of mathematicians. The PhD is new to the UK, compared to Germany or even to the United States (see NSF US Doctorates). It appeared at the end of the First World War and it was not until after the Second that a PhD became part of the usual preparation of a university mathematician... When looking up British mathematicians in the Mathematics Genealogy Project database:
Do not expect to find many PhDs before 1940.
Do not be surprised to find supervisors (advisors) with only a first degree...
The image of a PhD system has been present since 1850, there has been a PhD degree since 1920 and a functioning PhD system since around 1950.In the 19th century British university reformers looked to Germany for a model of the modern university and the higher degree was an element in the German system... In Cambridge there was no feeling that a research degree was necessary for its own graduates but the university created a Bachelor of Arts by Research for graduates from other universities; this could be completed in one year. This was not a popular degree and BritMath lists only one person with it, appropriately the unique Ramanujan...
By the beginning of the 20th century the case for a PhD type degree had been made and won — at least outside Cambridge (and Oxford). In 1917 representatives of the universities met and agreed that they would establish a PhD degree... However, deciding to create a degree is not the same as deciding that the degree should matter. There was no resolution to create a system in which the PhD would be an essential part of the preparation of the university academic. The system evolved without anybody planning it... Oxford was the first university to institute such a degree, although its choice of title, DPhil, was idiosyncratic. The first Oxford DPhil in mathematics was awarded in 1921. The first Cambridge PhD in mathematics was awarded in 1924 to an Australian Thomas Cherry.
