If I tell my therapist I cut myself will she...?!

No. Most therapists know that if they were to tell your parents something you told the therapist, you would never open up to them again. They want to build trust between the 2 of you, so you will open up to them They are trying to help you, but they can't do that unless you tell them what is really going on. I suggest telling your therapist, so they can realize the severity of the problem. I am 99% sure they will not tell your parents. Please tell them about it.

yeah, depends on age though, I went for one session, because of it, so my parents already knew but the therapist said everything was confidential except these things: If I am getting abused, if I tell her I am going to hurt myself, or I'm going to hurt someone else
so if I were you I would say I have in the past but not recently, because she might be able to tell your parents....I'm not sure though completely

I have seen a few psychiatrists and each one of them knew I cut myself, but none of them ever told my parents, but my parents already knew because they saw my cuts. I started cutting when I was 12 so I was not as smart about planning a location of my body to cut so that people will not see it as I am now. It may also depend on your age. Do you cut because you like it or are you one of those cutters that cry about their "devastating" habit?

she has a code of professional conduct everything you tell her should be in confidence unless you are a danger to your self or others - in which case her needs to alert your gp etc.
if you say you don't want your parents to know she cannot tell them without your permission and if she does you can make a complaint to her manager and get her in touble

source - floating around the UK mental health system for more years than i care to recall

It all depends on how old you are. If under 18, then they are duty bound to tell your parents. If over 18, then they have no rights to do so, as you are an adult, and entitled to have your confidentiality respected.

no i tell my phycological doctor everything he/she CAN NOT tell anyone anything you talked about. if you don't feel comfortable you always can change your doctor

Depends, do you still live with them? And please, stop cutting yourself. Why do it?

No, thats illegal unless she has your consent. Nomatter what age.