Note that UK universities place a lot of emphasis on master’s degrees. It would be rather unusual for a student to go directly from undergrad to a doctoral program at Oxford and bypass a master’s. Unlike in the US, doctoral programs in the UK rarely allow for much (if any) coursework. In fact, even master’s programs often require little coursework since students in the UK specialize more as undergraduates than in the US.
Also note that teaching opportunities are decidedly limited at Oxford…something to consider if you wish to go into academia.
If you don’t have a valid, compelling reason for wanting to complete a doctorate at Oxford – such as wanting to work with a particular professor or set of resources – you should look into doing a one or two year MSt/MPhil program instead. There are several sources of funding available, such as the Rhodes, Beinecke, Marshall, Chevening, Clarendon Fund, etc., though full scholarships are extraordinarily competitive.
This is true of any PhD program, including those in the US.
There are many reasons for a perfectly qualified applicant to be rejected, and there are very strong candidates that get shut out everywhere they apply, particularly in the horrifically competitive humanities disciplines. Perhaps the professor of interest is going on sabbatical next year and doesn’t wish to take any new students that year, or perhaps (s)he already has too many advisees from years past. Perhaps the department will admit someone interested in comparative literature and eligible for FLAS funding but not someone wishing to work on colonial American literature. Alternately, perhaps the department just hired two new faculty members in African-American literature and queer theory and wants to admit several students in those areas that year. There are several aspects of graduate admissions that are simply out of an applicant’s control, which makes it far less predictable than college admissions.