We also have civil partnerships in the UK, with all the same rights and benefits.

Yes the UK has "civil parternship" which is legally the same as marriage (except you cannot get civil partnered in the offical state religion/church).

Some countries (e.g. Ireland) have "civil partnership" laws which does not have the same rights as marriage.

Still, "separate but equal" is not good.

Yup, hence the (anti-)same-sex marriage campaign.