Many of the scholarship auditionees I spoke to had done singing grades 6 and above, with many working at grade 8 standard. However, this isn't a requirement, more of an idea of where you roughly need to at in terms of the technical aspect of singing. Levels of experience amongst scholars will vary, so if in doubt I'd say to give it a try!
Regarding non-auditioning choirs, I believe K_Man's description would be spot on for Oxford too. For example, I understand Wadham has a non-auditioning choir where to join you just need to speak to the musical director beforehand and you can then sort something out. They probably will still get you to sing, mainly to understand your voice better, though it would be more casual than the choral scholarship auditions.