How can I tell my cousin that she can visit but not her friend without being rude?

[Antst]

It is clear that she is inviting her friend. So the best thing to do is to acknowledge that. If you act like you don't understand that she expects her friend to stay too, you'll come across as passive-aggressive and the whole situation will get more complicated.

If you really don't want the friend to stay too, say something like, "we are looking forward to having you and our couch is ready to go! If your friend needs help finding a place to stay, just let us know and we'd be happy to help with hostel/hotel suggestions. I wish we could have her here, but there's only space for one person."

My advice though, is be cool about the friend. It is understandable that you want to spend time alone with your cousin and you can tell her that ("we hope you'll have time for some family time"). But it is part of the culture in the UK to travel with friends. Your cousin probably doesn't mean to be rude... It is normal in the UK to take a friend along. Also, if your cousin is with her friend, then you won't have to spend so much time and money looking after her. They can entertain each other. Put them both on the floor in your living room and they'll be fine. This is one of those situations where the best thing to do is be gracious, even though it would be understandable if you thought your cousin was being pushy!

Good luck.