Sorry, you're right, again, about he Scottish difference, In England, the first year of a degree course is implicitly ordinary. After the first year, a board examines the student's record and determines if they are allowed to proceed into Honours, which is the second year.
While I think that you very much should say that a cum laude degree is equivalent to a 2-1 and a summa to a first class with distinction, I'd hesitate about mentioning Phi Beta Kappa for two reasons. Firstly, it doesn't correlate to anything here. Secondly, there's a local suspicion of membership in societies that aren't State-backed (ie, Royal academy). Phi Beta Kappa is just too close to something like the Masons, which doesn't have an entirely positive association here (the comparison is not odd since PBK began as a secret society and continued as one for decades until a member outed its presence in the mid 19C). While some universities treat entry as simply a matter of the right GPA, others use it as an elite group requiring invitation. You don't want to have this confusion impact your CV (ie while it's good to tell you remployer that you're smart, I'm not sure it's a good strategy to say that you've been a member of an invite-only group).