Hello again, thank you again everyone for your comments. It seems this is a contentious issue with differing views.
Yesterday was a long emotional day but I am pleased to report that my daughter and I have found a way back to each other and she's home. 
Firstly, I would just like to answer a couple of comments regarding some posters thinking my daughter had 'left' home, that she seems to be from a broken home and also about my sons role..
Firstly, Yes it was a 'runaway strop' not an 'I've left home', she took 3 pairs of knickers, 2 outfits, a bag full of make-up and a handful of books! She didn't even take her phone charger! I hardly think that says, 'I'm leaving home'.
DinosaursRoar No, she is NOT from a broken home and Yes, the boyfriend's parents DID & DO KNOW that. Single parent does not mean broken home, nor does pushing boundaries, teenage rebellion, having a row with your mum or a runaway strop! Her father is dead. She has been raised, alone by me since she was 2, in a loving, caring home with rules and boundaries that have kept her safe and secure and able to grow into the amazing, beautiful teenager (because she's not yet an adult) that she is. I also said she had few 'friends' her own age, I never said she didn't have 'hobbies', she has a good and full life but it's been a different life to many her own age due to health issues. She has hobbies that are related to what she wants to do in her future and these are mostly attended by adults, I haven't nor would I force her to change hobbies just because there's not many kids around.
Regarding my son, well he's had his own problems. He dropped out of Uni because of various lifestyle choices he made and has spent many years being (by his own admission) totally selfish. He is 10 years older than my daughter and when she was going through many serious health issues and operations, he was off leading a hedonistic lifestyle and only giving a damn about himself, he wasn't there for her and she was very hurt by this. It is only VERY recently that he has settled and is trying to put right past wrongs, therefore, he tried too hard to please her, taking her side and indulging her teenage strop because he wanted her to forgive him. He admitted yesterday he should have handled this better, that he should have called me and asked for advice, but she was begging him to be on her side and he didn't want to hurt her again by taking an adult stance with her.
Anyway, my daughter and I had a long, long talk yesterday. After calming down on here the previous day, I was able to understand myself and how I was feeling and I was able to explain that to her. I understand now that what she was fighting against was what she saw as control and that is my fault. My fears for her to not be hurt, to not make my mistakes, and perhaps my over-protection because of all she has been through, have not been portrayed to her as fears, they have been portrayed, wrongly, as control. That was never my intention, yet somehow I couldn't see that I was doing it.
We have come to a new understanding and reached compromises that suit us both. She will put her studies first until her exams in June. I will reach out to the boyfriend and be more understanding of their relationship and he will be spending more time with us, I will also be taking her to the Doctors to discuss contraception. There were many more things discussed, of course, and we are both very happy with the outcome. She does understand that she still needs guidance, boundaries, rules, like be home by a certain time etc and has accepted that. Equally, I have accepted that she is in need of more faith and trust in her and her choices and I will give her that, Always.
As for the boyfriend's parents, I sorry but my stance there has not moved. I always would phone another parent to check they were ok with something. That is just me, I know, my principles, my way. I do live by 'treat others the way you would wish to be treated'. I don't think that's wrong and I'm sorry some of you do.
So this is me, thanking you all, good and bad comments, I am hopeful for my little family's future and wish you all happiness and good health.
Much love,
MJ x