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Wow I am so sorry your daughter is going through these problems it must be heartbreaking to see and experience second hand for you and your family.
First off she needs to be seen by a psychiatrist for an evaluation and/or counselor for routine therapy, (which is basically nothing more than talking through her problems and learning different coping strategies she can rely on in a stressful situation).
I realize in the UK you may not have great access to child psychiatry but it does sound like your daughter needs professional help. If you are unable to get her in to see a psychiatrist (MD), then at least start with a child therapist. The acting out in extreme as well as the fear of being alone at night are most likely related to what she is experiencing at school.
It kind of makes me wonder if there is something more than the bullying going on, if there had been a traumatic experience for example....that you may not know about....however bullying itself is enough of a trauma to cause issues like this.
She needs a major boost of self esteem so that the bullies in every school or situation she will encounter will not immediately sense that she is weaker and thus an easy target.
If not yet involved in after school activities that she enjoys and where she can find other kids that enjoy the same activities this is a great place to start. I love physical activities such as dance, martial arts (really good at working on self esteem!!), etc...it doesn't sound like she is ready for a team sport yet as she needs to find out how to work well with other kids first before placing her in a team setting that may set her up for more ridicule.
The extra quality time for her is vital providing her with added attention from you and her older sibs, but she needs some peer contacts as well that she can consider friends and that she spends time with outside of school.
Taking her out of school is not the answer in my opinion even though your first instinct is to end the exposure she reports is causing her "pain"...learning to deal with the taunts is vital for her life experience later on.
Personal care is not optional thus you need to make some rules about what she needs to do around the house and stick with them. Having structure and a safe place at home is very important to a child who doesn't feel great when they leave the house.
If she doesn't comply she needs to have things removed such as TV, or games, etc...you know the drill. Try not to be "too easy" on her at home as you know that she is going through a hard time.
If you do have any history of mental illness in your families she may be starting to manifest something like depression, as this and other mental health disorders can start in kids. Thus the psychiatrist as important in teasing out this possibilty vs just your daughter as someone who is extremely shy.
Putting her in a position of authority, (caring for pets, younger kids, doing household chores for $), may help her as well although at 8 she is a bit young for this...however giving her more control over things at home may empower her, (choosing things for meals, at the store for herself, things to do with the family, etc..).
Here is a website for you to look through http://www.kidpower.org/library/article/prevent-bullying/?gclid=CKX7z-656rUCFYfJtAodtjQA6Q
Bullying is real and takes away her sense of control and power but as you have found out just removing her from the bullies without working on what makes her vulnerable won't work. You have to work on her from within to make her armor stronger. Her behavior now by acting out is a call for help. There may also be bullying support services in your community as people are starting to pay closer attention to the detrimental effects on a child. It is never ok for another child to make yours feel bad but unfortunately is a common thing. Bullies feed off of other kids they see as weaker in an effort to empower themselves....usually there is something wrong with them (the bully) at home and they use this to help their own problems....
Even though her bullying hasn't included anything physical, nasty words can cut just as deep in a vulnerable child. I wish you the best of luck and please feel free to respond when you receive word of my answer so that we may chat if you feel you would like to.
I apologize your question has been up for so long. The UK site is just getting off the ground and I for one do not check it regularly so I apologize if this is your first contact with Just Answer. Thanks!