As we have established there is no legal recourse. At 16 if your daughter decides to move out and live with the guy there is nothing you can do. Not everyone would agree that this is appropriate at this age but that's how it is. I remember reading about a young girl going to live with a 49 year old who had been her teacher and feeling sorry for the family:
Girl of 16 moves in with her 49-year-old RE teacher then informs parents by email| News | This is London
I have included this to share a little bit with our non-Brit friends of how hard it is for parents of this age here.
You could try banning this but in practical terms how exactly would you ensure this was enforced? You can't exactly ground her forever. You already know that she will probably see him behind your back. In the UK, governmental lead and cultural shift has led to a generation of young people who are strong at demanding their rights and can sometimes be very difficult. Good things have come out of the increasing view that children should be heard and their views count but I do think it isn't properly balanced and adults' options for trying to discipline and protect children have diminished.
I can fully understand how frustrated you must feel. I can also understand where our lovely USA advisors are coming from. However I feel that in practical terms what would work in the USA simply wouldn't here.
We may feel that at 16 our children are children but the law and current culture puts them in an awkward half-way place where they have most, but not all, the rights of an adult but are still expected, though not required, to continue their eductation. Even when my son was 21 his university loans were based on our ability to help him financially even though we have no say in his actions as an adult. So we parents have to treat them like adults but support them like children. Not always ideal.
In some respects she is still your little girl. Your heart wants to protect her but you have to use your head. Since the things you might want to do will probably not work you have to find a compromise situtation.
If you take the 'not while you live unde my roof' stance then you run the risk of her deciding to move out. It is your choice whether you are willing to do so.
I can remember when my daughter was 16 how she felt much more adult than I considered her to be, but the law supports her and the media and cultural norms reinforce her view. I wasn't prepared to butt heads with her and push her away by trying to be as controlling so I had to get her on-side and treat her as an adult, get her to accept advice rather than rules, whilst at the same time she was financially dependent like a child. Not fair on us parents but it was much better than having her leave home in a huff and abandon her education. She's 21 now and she has turned out great.
Whatever you decide is the way forwards I wish you and your daughter well.