Virginia Woolf tells her audience that she is going to make 'use of all the liberties and licences of a novelist' and immediately refers to the two places, 'Oxbridge' and 'Fernham', which she has invented for the purpose of her lecture. 'Oxbridge' (an amalgamation of Oxford and Cambridge) is Woolf's fictional name for the Universities of Cambridge and Oxford, and 'Fernham', her fictional name for Newnham and Girton Colleges. 'Oxbridge' may, therefore, be seen as representing the University system in general, while 'Fernham' may be seen as representing women's higher education in general.
In using 'Oxbridge' as the name of a fictional university, Virginia Woolf is following in the footsteps of William Thackeray who used it as the location of the fictional Boniface College in his novel Pendennis (1849). The term 'Oxbridge' has passed now passed into general usage to mean, 'either Oxford or Cambridge University' or 'both Oxford and Cambridge University', and can be used as either a noun or an adjective.