Thank you all for your replies and I am grateful to ARV for sharing her experience and pleased that it had a happy ending.
One of the posters mentioned passivity and I think there is some truth to that. I have told very few people of my concerns in RL, but my aunt in law, whose is a wise woman, said she thought DD might 'need someone to lean on', which is fine if the person you lean on can be trusted to take care of your interests and welfare.
Another poster asked what I had done to teach her this behaviour. I have asked myself this question many times, but her sisters are the opposite - very focused and determined and in no way passive, and nor am I. They describe themselves as 'strong independent women' - their mantra, which they often quote, which DD1 also claims to espouse, but doesn't really 'walk the walk'. DD2 has a boyfriend and this appears to be serious, although it's early days, but the dynamic is totally different. There is no way she would put her life on hold for her boyfriend and there is no way that he would expect her to.
To be fair, it is just under 2 months since DD1 graduated and a lot of young people don't have a career mapped out, especially if they are arts graduates. However, she didn't go to the careers advice centre at uni before she left, which might have given her some pointers. Also, she is an intermediate Cordon Bleu cook (she did a course during her gap year), so could probably find work in catering, but says she can't do this, as she would need to taste the food, which she can't do as she is vegan.
I imagine that this is a critical time for the relationship, in any event. When they were both students, life was mapped out for them, and they knew in which direction they were heading. They both had the same goal of graduating. Not so now, at least not for DD.
There will be a crunch point in another year when BF graduates. My understanding is that his parents were prepared to pay the other 50% of the cost of buying the house after I pulled out (his GPs had given him the 50% for his share), but regard it as an investment, which is fair enough. The house was a good price - the seller picked us for a quick sale as it was a cash purchase - and they will make some profit probably if they sell it. Or they might rent it out. I don't believe that BF or his parents see it as a potential 'matrimonial home'.
The same wise aunt - who is a bit cynical - thinks BF might have targeted DD because she seemed to be from a wealthy background. DD said people in the house at uni, where she met him, had been googling her house on google earth; it is nothing grand but a lot of land and a tennis court and we have a holiday home(not a stealth boast and we have a big mortgage but just to give the full picture). There seems little doubt that the idea of buying the house was his idea and I was expected to pay for it, or at least for half of it.
Initially, I wanted to help and I wanted DD to have a home so I knew she would always have this security, but then I began to have doubts about him and to be worried that she would be tied to the house and to him and that there would be no incentive to find a job and her own way in life. I love my children and want to support them, but also to encourage them to find their own way and to become independent, as DH and I did - we didn't have any handouts from our respective parents. Anyway, I think that if he really loves her, he should love her regardless and that it should not be dependent on her buying half of the property or any future property.
I have paid DD her allowance for a further 3 months and signed over the car to her and paid her motor expenses - tax and insurance and servicing and MOT - for a year, so that she is able to get to any interviews. I also still pay her mobile 'phone contract. She also has some money from the sale of her horse, so about £5,000 in total, which is a bit of a cushion, but I suppose will run out after a while if she doesn't get a job.
My DD, who was to have been a joint owner, now has no say in what happens to the house. She doesn't seem to mind and says it still feels like home. She bought some items on holiday for the house and has taken one of our tvs and some pans etc that I bought for her, as well as her chef's knives. BF and his parents seem to be making all of the decisions about the decor - paint and carpets etc. Originally, DD was quite excited about the colour schemes and was on Pinterest etc but this all seems to have fallen by the wayside.
There are certainly some self esteem issues there, and getting a job would hopefully boost her confidence. As far as I know, BF is encouraging her to get a job - well, he would wouldn't he - last time she came back she took all of her certificates as BF had told her that she needed to have them to apply for a job.
I have not suggested to DD that she is correct not to take the ADs. On the contrary, I suggested that she should see her GP, but she is adamant that she doesn't want to. TBH, she seems like a bit of a lost soul at the moment. She went back yesterday and her parting words were 'I love you. I will be back soon'.
Sorry this is long!