Hi Alsa,
Can I check which Key Stage your daughter is in? If it's KS1 (7 years old) then the SATs are not 'as compulsory' as at KS2. Teachers can use the reading test, for instance, to help them to double check their own ongoing teacher assessment, but there's no legal requirement to do so. The same page (p24) as Serrakunda27 mentioned above, but in the KS1 booklet, tells you more about the reasons for disapplying. I would hazard a guess that your daughter would come under the first two bullet points on p24. The KS1 booklet is here: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/754076/Key_stage_1_assessment_and_reporting_arrangements.pdf
Also see p25 about Access Arrangements, especially bullet points 2 & 3. One Access Arrangement I've heard of, that reduces stress and caters to needs, is that in a smaller quieter room, someone could help her by reading the test out loud to her, reading the questions and jotting down her answers. They would gain an overview of her listening comprehension in this way. For her own reading, if she is not yet reading at an age-appropriate level, fluently, then she is highly likely to struggle and "they are working below the overall standard of the KS1 tests (and are considered to be unable to answer the easiest questions)" (ARA p24).
The 'Teacher Assessment Frameworks' for reading, writing and maths are the only compulsory things for them to assess against at KS1 - these are lists of skills and knowledge that the teachers do not need to run tests for. They can confirm ongoing judgements against ongoing activities and work they've set previously. This is where it is different from KS2. See p2 bullet point 4, and top paragraph of p3 here: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/740343/2018-19_teacher_assessment_frameworks_at_the_end_of_key_stage_1_WEBHO.pdf
The school's Senco/Inco should be able to advise more (maybe ask this helpful classteacher to arrange a chat between the three of you?). The school receives Pupil Premium Plus funding for your child, so there should be access to additional funds for exactly this sort of support, and I would hope some to address the learning gaps and anxiety. Your Local Authority's Virtual School Head has a role to advocate for these children too:
"Virtual school heads promote the educational achievement of the children who are looked after by the local authority they work for. They also manage pupil premium plus funding, which is an extra payment that schools receive for each looked-after child, and previously looked-after child, on their roll."
I think it's worth going to the Senco/Inco and discussing access arrangements or forms of teacher assessment that allow your daughter to truly shine. After all, even if she is disapplied, the school still has to report her data in amongst everyone else's and there is a very big national focus on children who receive Pupil Premium (incl her), so it's in everybody's best interests for all sorts of reasons. My concerns next would be: and so what next for helping her to cope with her difficulties, deal with anxiety and to catch up with her peers as much as possible??
I hope that helps a bit.