The college system does not work the same in Oxford as it does in Cambridge. While Cambridge do admissions on a college basis, Oxford you apply to colleges but there is much greater equality. So whilst some colleges may have better results, in general the quality of applicants, and hence the requirements, are the same.
In terms of the actual requirements, Oxford does not require further maths but it's *highly* recommended and they'll expect you to catch up what you haven't done. They'll also likely want to know why you haven't done further maths, which is presumably to your college not offering.
So yeah, no colleges require it, but it's undoubtedly helpful/needed to do it.
Edit: As the above poster points out, this only applies for a few degrees e.g. maths which further maths is useful for.