DD is the same, and was even the same with adults..I think daycare has helped a lot, because I am not there with her so she can't cling to me and stick with me like she does at playgroup, she has to rely on her carers and they do lots of group time activities where she has to interact with the other kids. Often when I go to pick her up she will be sitting in the sandpit playing by herself..lol. But at least I know she has had the opportunity to be surrounded by other kids and interact with people other than myself.
I know I was a pretty shy, reserved kid and would happily spend hours reading or playing by myself, especially once I hit high school it was hard to make friends (possibly more so now I'm an adult!), and I want to give her the opportunity to develop the social skills she is going to need in later life. The hard thing is that she is worse when I am there!