score:4
The Oxford colleges individually handled matriculation through Responsions and other exams:
Until 1887 all undergraduates were required to take classical pass or honour Moderations before proceeding to a final school, and this cut into the time available for science. Even when scientists were exempted from Mods. 'compulsory Greek' in the examinations--Responsions or its equivalents--that qualified undergraduates to embark on the NSS was relatively demanding.
...although the same web page also states:
No university entrance examination existed at Oxford before 1914. ... Admissions were in the hands of the colleges, and the University was required to matriculate any man whom a college chose to admit.
(The History of the University of Oxford vol VII, 'Nineteenth Century Oxford')
Dublin and Cambridge appear to have had similar procedures at that time.
The Wikipedia entry for Durham University says:
The university opened on 28 October 1833 with 19 "scholars" and 18 "students" on the Bachelor of Arts course and 5 students on the theology licence course. The university was the first in England to introduce matriculation examinations, although these had been in use at the University of St Andrews and Marischal College, Aberdeen since the 1820s