Hi,
I've also been an aupair (2005-2007) and It Can be a bit difficult at the beginning until you settle in and make friends , know the area and how everything works in UK. I am
Not sure how long your au pair has been in the UK for , if she has friends, knows the area etc.
The family I worked for was great and they wanted me to be around all the time and used to take me out everywhere with them in the weekends , especially the first couple of months. I felt a bit awkward as everything was new to me and felt Like they need their privacy but they always insisted I go out for family dinners, picnics , parties and I did that for a while until I made friends and started going out with them instead
) but still attended all family dinners, birthday parties , always went out for dinner for my birthday etc.The family always treated me like a member of the family , an older child if I can say so and they still are like a second mum and dad to me . You need to remember that she is by herself , no family or friends so she might feel comfortable being around you and your family instead of being alone in her room. Try encourage her to go out in her free time and explore London ,make new friends ... Maybe some of your friends have au pairs / nannies and you can put her in touch with so she can hang out , out of the house
) or ask her if she would like to take a course ( English or something that she s passionate about) and that will give her the opportunity to go out and meet new people .
I am sure once she has made some friends and is a bit more confident she will always be out and about .
Also If you don't feel comfortable with her being around ,she doesn't feel part of the family and that stops you being yourself then maybe she is not the right au pair for you.
Good luck! Hope everything works out!