EEA national in a civil union with British citizen

I am an EEA national, planning to move to the UK. According to the benefits regulations, I cannot claim benefits as an EEA national in the first 3 months. However, if I am in a civil union with my partner who is a British citizen, am I eligible for such benefits even in the first three months? Also: if I am not eligible, would it affect my partner's housing benefits in this period if we declared that we live together?
Thank you in advance.

Yes, the rules are different where your spouse is British or a person with settled status,