What's the Name of That Book??? discussion

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The High House
SOLVED: Children's/YA
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SOLVED. YA Series set in Scotland/UK featuring a girl in high school and after [s]
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oh Yes - it totally was! Thank you so much - it has been driving me up the wall for the past few weeks. Hooray!
I read a series of books when I was maybe 12 so that would have been in the late 1970s. They were set contemporaneously in the UK. I think maybe Edinburgh. I want to say the girl's name was Emma or Gemma but I might be making that up. I remember her studying for her O-levels in one of the books. In the last book (that I read anyway), she had finished school but I'm not sure whether she got a job or went to university or both. I know she moved out to live on her own.
I have a feeling the series might have started when her parents died and she had to move to Scotland (?) to live with her aunt (?). So a lot of the stories were about her finding her way and coping with the loss of her parents and fitting in. There was a romantic thread which was more apparent in the last book because she was 18 or so by then.
I want to say she was a redhead but I might just be confusing her with Anne of Green Gables!
I don't remember the title or the author but I read them when I was at school so they were either in the school library or the local public library. I'm in Australia so they were popular enough to reach our libraries.
I'm sorry that's so vague. I hope someone can help. I'd love to revisit these books if only I could remember their titles/author.
Thanks all.