I have been having problems with my child since she was 2, due to some unfortunate events at that time. However, she has had a pattern of behaviour since then and as she has got older (now early teens), she is getting even worse. I am worried that this constant behaviour is actually now affecting her, as she is missing out on many good things in life due to her behaviour, i.e. she gets grounded by being cheeky and slapping me and talking over me. At the time, I threaten that she will be grounded if she continues her behaviour, she screams and carries on and after much time has passed and many threats to the consequences she gets grounded.
When the time comes and she has to cancel her arrangements she screams she hates me and it is all my fault. She then tells her friends that I am a crazy women, and makes out that I am the one screaming all the time, and that she is punished for nothingand totally innocent. (This she says to me as well). She then denies in my face completely, that she did not hit me etc, etc. She also once threw my mobile phone across the floor in front of me, and in the same instant, denied completely that she had done this.
I try and talk to her, to teach her and explain what she is doing, but she talks over me, i.e. over and over, leave me alone, leave me alone, so she drowns out my voice and this goes on and on, so she never learns from her punishments and never listens to reason, and things have got so bad, that I feel I do not want her in the room with me a lot of the time. However, I also worry, that she is creating a permanent bad behaviour pattern forherself and she is losing out on a qualitly of life, as she is creating friction for herself and myself all the time.
However, she lies to herself, and never ever acknowledges what she has done, never, and in her mind, it is all my fault and that I am a terrible women. (Actually, if she only allowed, I could be the most amazing mother to her). But, she rejects it. (I am a single parent).
What can I do? I am beside myself. I have gone to a therapist, and they do nothing.
I am just amazed at how she cannot even see what she is doing. It is almost like she in her mind feels that she is the victim and she can't wait to leave when she is of age. She just does not register at all what she is doing to herself and me.
(Her father is not in our life, however, he also tells lies. He rejected me when I was pregnant and washed his hands off us.) Now he goes around telling everyone that I kidnapped her and hid her from him, i.e. he is the victim and he believes it. Is this inherited?

Telling lies is not an inherited trait. I know that many people feel that corporal punishment is wrong, but a swat on the behind would get her attention and you seem to have allowed her behavior to go unchecked for so long, to her it is a normal response to yell over you and act out when she knows she can get away with it.
Her father should have shared in the child rearing experience and is partially to blame due to his absence of a father figure and role model, but you are also to blame, get some guidance from a child counselor now and you and she will be better in the future for it.
I hope you can get the help you need and it's obvious you do care or you would not be asking for advice, good luck to you.

Lying, kniving, and thieving are all one thing. Perhaps explaining one will help all 3.

If they have one of these. They have them all.

You both need to talk to a professional therapist. The sooner the better. This is a very serious situation. Children lie for two reasons, they are afraid of being punished or they don't care very much about anything anymore - especially your opinion of them.

I have had a similar situation with my son who is now an adult. I have been doing my own research on this and based on what you are describing it sounds like your daughter has a personality disorder. It is very hard to diagnosis. I went through what you are going through and my heart goes out to you. There are psychotherapists that specialize in this disorder. Get the book Walking on Eggshells that will help you understand this disorder and give you some resources to help you. Don't take her behavior personally it isn't about you it is her issues but she doesn't see that. Good Luck!