I am a teenage girl living in england wishing to become a buddhist nun?

First find out where the nearest dharma center is that has a resident teacher. This will teacher will be an older Buddhist monk or nun in any of the traditions. They teacher may live in that city or they may advise the dharma group and occasionally visit it in person.
OR find a Buddhist temple, but be advised that sometimes they do not speak English .. they would be there to serve a large Asian population

Also understand that when you use the services of a dharma group or temple you are expected to contribute financially. That is karma ... when you take, you have a obligation to give back.

So find a teacher and DO the practices that your teacher gives ... do them daily. After about 5 years of being a Buddhist, only THEN can you determine if this is a lasting appeal for you. Many monks will NOT give you the samaya vows (monk/nun vows) until you have shown them - through 5 years of guidance from them - that you ARE serious and WILL stay serious.
btw, did you now that as a Vajrayana nun, you will be taking over 250 vows, rules for how you live, things as simple as when and where and how you eat or blow your nose? And that you need to follow ALL of those little vows?
The life of a nun is not easy, it is not the peaceful utopia you think it is

And if you are not happy now, you will not be happy being a nun either. That is because our happiness/unhappiness depends on OUR state of mind, not on any external circumstances. So where you go, you take your happiness/unhappiness WITH you.
And since the life of a nun is physically uncomfortable, it is far easier to be dissatisfied as a nun than it is to be dissatisfied as a not-nun.

And be patient. It takes 3-8 years before you even START to benefit from the practices you work at every day. Don't expect Buddhism to be a free or fast ride out of unhappiness.

Lastly, there is an old saying in Buddhism .. "Wherever you ARE, THAT is where you do your practices." And "Start where you are".

So start by attending teachings This site lists dharma groups worldwide, so find the one that is nearest to you or that you an make it to, and that gives you access to in-person teachings from an actual ordained Buddhist monk or nun. Perhaps you might wish to get a part-time job so you can afford to make the offerings that help provide the housing and help feed the teacher.
As a foreigner in a foreign country, you would be expected to pay your own way. Unless your teacher ordained you and sent you to that convent. You cannot just go over there and expect them to support you ... and you would need to learn their language well before you went over.
http://www.buddhanet.info/wbd/

You may go to London Fo Guang Shan Buddhist Temple. I guess they won't ask your donation. They already have very good donations.

This is their website. You may ask them about your conditions.
https://www.facebook.com/londonfgs/

I am native Indian, an ex atheist and now a Hindu. there is something Buddha said which you might know "worldly desires are root cause of all sufferings but the desire of renunciation must come from deep inside"
you have a long way to go, there is no hurry. you can practice Buddhism at your home like you can do meditation in your room. I respect your thoughts!

But you sure TYPE english pretty good

I may be out of it, but I think Buddhism values honesty. You need to start being honest with your parents. You might find they have more potential than you ever knew.

I also believe Buddhism is about patience. At fifteen years old, you have not had an opportunity to learn true patience. Patience is going to a teacher to learn a system of meditation and being told to go away, and staying around outside that school for fifteen years until the teacher finally tells you to come in and start learning.

You also need to consider that everything you may currently be thinking might be completely wrong. This doesn't mean you stop what you are doing; it means that you discuss your ideas with others and then you learn from their responses and see what works and what doesn't work, and you then chart your course accordingly.

I am a teenage girl living in england wishing to become a buddhist nun? Move to Ural Mountains and become Ruski Orthodox. Or wait in England as Britain will be flooded and Brits will move to Russia as Vyacheslav Krasheninnikov predicted.