I have always thought my Dd was pretty sociable, always makes friends at the park, soft play etc. Since she stated at a new school last August she has not really made any friends.
Recently she told me she never asks children to play they have to ask her, it is school holidays where we live and there were children playing out, eventually after trying to get her to ask to make the first move I asked the children if she could play with them, she said hello and Introduced herself and then hid behind me and would not make an effort.
Both my husband are a little shy but I don't think I was ever as shy is she is being now. We do not live in the UK and although she speaks Dutch fluently I wonder if the language difference is making it worse.
From what you say, the other DCs were just quicker at becoming comfortable within the new environment. It's encouraging that her classmates aren't ignoring or ostracising her, it doesn't sound like the language issue is at fault, they may be perfectly sociable but they probably all just get stuck in whereas DD finds it hard to initiate play.
Have you talked to her teacher about this?
I wonder if you are finding this upsetting because it brings back memories of your own school days.
As LastingLight suggests, perhaps arrange regular playdates with one DC in particular then slowly include other classmates.