In June 2020 Ethical Consumer viewed the Oxfam website and saw that it sold bodycare products, but not own-brand.
In August 2018 Ethical Consumer received a questionnaire from Oxfam which stated "We do not retail own-brand cosmetics, toiletries or household cleaning products. All brands that we buy in must comply with our palm oil policy, as well as be cruelty free certified, with approximately 90% of our hair care, body wash and cleaning products being Vegan certified."
No evidence was found to suggest this was not still the case, although no publicly available policy was found. While Ethical Consumer deemed Oxfam to have a positive animal testing policy, it did not explicitly state this included a fixed cut off date for animal testing, and so it lost half a mark in this category.

Reference:

https://www.oxfam.org.uk (1 June 2020)