You could look at the options available to home educated children, though there are probably additional paths open to your daughter as well. I don't know whether these options are appropriate for your dd, but here is some info in case it might be:
Home educated kids typically do IGCSEs, which are exam-based, because of the difficulty they experience in getting controlled assessments approved. They sit the exam as a private candidate in an exam centre, which could be a school or other centre. It can be tricky to identify a suitable centre for the subject desired, so teens are usually advised to find the centre first, before beginning their studies. Then you know which exam board (and therefore which syllabus) you are preparing for, and which dates are possible. (There is no particular need to sit all the exams at once at the end of Y11 if a different plan seems better. Home ed kids typically study a few subjects intensively, sit the exams, and then move on to another few subjects.) Preparing for the exam can be done independently, or using a tutor, or via an online course.
Here is a wiki about the topic. At the top of the page you'll find a link to a very busy email list where you can chat with other people who are doing the same. You may even find some people there who are in the same situation as you, or in the similar situation of having home-based education funded by the Local Authority. nwilts-he.org.uk/he_exams_wiki/
Ideally your daughter could drop some less relevant subjects at school so as to free up more time for the extra academic subjects she needs to do, rather than having to do them in her own time on top of a full school day.