From what I can find out, I don't think that marriage of 1st cousins has ever been prohibited. The main prohibitions are those in a direct line, all the relationships within the second degree (ie closer than 1st cousin), brothers and sisters whether full or half blood, and also people acting in place of parents. This last one is definitely current now, though I'm not sure how long that has been in, as things do change.
In my family I can find three marriages of first cousins in a fairly small chunk of the tree (19th century), and I know of first cousins who married about 25 years ago quite legally.