All the posts above are excellent, especially Lucid's. All cathedral musicians are expected to perform at a professional level. Cathedral organ scholarships are a training position, but any mentions of Grade 8 should probably be taken to mean "at merit level", maybe higher. As Tenor Viol suggests, it may well be that something near ARCO standard is what is really desired, although I think most Directors of Music will to some extent tailor the job to suit the holder's ability. The fundamental question going through any interviewer's mind would be, "Does this candidate have the potential to become a professional cathedral musician and be useful to me?" At the top half dozen Oxbridge colleges the standard expected of the organ scholars is as high as it comes: fully professional already, studentship notwithstanding. I am open to correction, but as I understand it, in the less prestigious Oxbridge colleges the organ scholar is more or less wholly responsible for the running of the chapel music. This must be valuable experience, but I do wonder whether those posts can really equip you to cathedral standards in the way that working under the top choir directors can do. Working with children (as opposed to undergraduates) is a vital part of the skill set.
In a former era, when the organist and choirmaster were the same person, the late Sidney Campbell worked his way up the tree, from half a dozen parish churches, via Southwark, Ely and Canterbury Cathedrals to, finally, St George's Chapel, Windsor without ever having been an assistant to anyone. That was quite a remarkable achievement and extremely unusual, if not unique. Nowadays, as already noted above, the choral directing and organist roles are usually separated and in recent years there have been cases where a Director of Music is not an organist at all, but has been recruited from outside the cathedral orbit because of their proven experience with singing and choirs.
All this notwithstanding, the routine career path for most cathedral organists these days is Organ Scholar >>> Assistant Director of Music/Organist >>> Director of Music. For someone not brought up in a cathedral environment as a chorister (as many organists are) it may be that a cathedral organ scholarship is the best goal. What counts is the ability, or at least the clear potential, to cope with playing for cathedral services to a fully competent standard. Going to a conservatoire is certainly not essential, although exposure to the sheer quality of future international celebrities and other awesomely talented musicians can be a stimulating (not to mention sobering) eye-opener to the standards one needs to be striving for.
My own organ scholarship was so long ago now that I can't remember my audition in detail, but some of the things I had to do were:
1. Transpose an Anglican chant at sight. (Sounds easy, but this one was full of chromatic elephant traps and I made a right pig's ear of it - I believe it had been an RCO transposition test in 1910 or thereabouts.)
2. Sight-read a piece of choral music in open score (i.e. on four staves).
3. Play the accompaniment of Herbert Howells's Like as the hart at sight (while the organist made some God-awful noise in my ear that approximated to singing).
4. Play the accompaniment to some Magnificat or other (Harwood in A flat?) while simultaneously incorporating the four vocal parts (again at sight).
5. Conduct the organist while he played an anthem.
6. Play a hymn at sight in a manner suitable for a congregation of 800.
7. Play an organ piece of my choice.
You will note that, although important, playing organ repertoire was only a tiny part of the audition. What was really being tested was my range of musical skills. However different today's auditions might be (and I suspect I had it quite easy), I'll bet that is still true.