Yes, I understand how you feel. My DC2 (DD, 3yrs 5m) will be starting Kindy in a couple of months, and I am slightly dreading it (not in the UK).
She is very shy, although a total character around people she knows. She is very much a Mummy's girl and hates being away from people she has a close relationship with.
However, bigger picture, I know this will be really good for her.
Your daughter being panicky when she can't see you in the park is totally normal, and no reflection of how she will be at nursery. At nursery, she will be in a safe environment, with people (albeit not her Mum) designated to care for her. In the park, when she can't see you, there's no-one else, so it's normal for her to feel panicked if she can't see you.
The initial settling in might take a bit of adjustment, but she will build bonds not only with her carers, but also with her peers. She will make friends, and she will feel safe. And people who work in these places do so, for the most part, because they actually like children. :)
My DS, who's older and a completely different personality, has absolutely thrived in the environment I am sending DD into, and so it's easy for me to have faith in it. I can see that it's not so easy for you, however you're obviously sending her there for a reason, and you really just have to have a little faith in both your decision, and in her.
And the other thing is that early childhood education is really, really important. It sets children up to learn. Children who participate in ECE before going to school statistically do better. It also helps with their social skills and builds their independence. And all of these things build their confidence and self-esteem.
These are all the things I remind myself of, when I'm having a wobble about her stating. She - and you! - will be fine. :)