I’ve scanned the obvious regulations and can’t actually find anything (RFU) that prohibits mixed sex teams, other than reg 15, but that is specifically up to and including U18, so arguably once beyond that you can (or I can’t find the bit that says you can’t.
Related, in GMS (RFU Game Management System, player registration etc), each Club team has a gender set, so Male, Female, Mixed etc so clearly there is an expectation that a team complies to that - although don’t think it would actually stop you registering. A male player in a female team, and vice versa.
The below article does exist on the world Rugby site, so a clear guidelines, and reasons why, but not a categoric no. Suspect World Rugby guidelines would be enough reason to say no?
http://playerwelfare.worldrugby.org/?documentid=117