Well, Bertie Wooster was wont to refer to 'the dear old Alma Mater', and my impression is that he was referring to his old school (public, of course, but never specifically identified) not to his university.

The thinking that led to the term Alma Mater is apparent, but I am intrigued by the similarity to ‘matriculation’ which: (borrowing largely from Wikipedia to save my sprained thumb – a whole other story) refers to the formal process of entering a university, or of becoming eligible to enter by acquiring the required prior qualifications.

In the ancient English universities of Oxford and Cambridge, the term is used for the ceremony at which new students are entered into the register (in Latin matricula) of the university. From that point on they become members of the university.

In England and Wales until the advent of the General Certificate of Education (GCE), Matriculation (usually abbreviated "matric") was the examination taken to earn the right to enter university. Unlike the GCE exam, it had a number of compulsory subjects and all had to be passed at a single sitting.
In Australia, Matriculation is currently the name of a university entrance examination.

As an aside, the UK gov. is considering reintroducing a matriculation type of examination, such as is already in use in parts of the EC.