That's something like '2nd cousin once removed' so as 4get says it's not illegal, but,again as 4get says, I wouldn't.
Did youb grow up knowing she's related? I mean, are you a close family who get together often? If you've known your related since you were kids and grew up together that may cause problems and friction within your families, in fact your relationship may cause you both to re-evaluate your family dynamics anyway. There was a report on Radio 4 last week about this subject and several couples in the same situation as you no longer have anything to do with their immediate families so be prepared.
That said, I wish you and your partner all the best and that you both are very happy together