A statement is necessary to help a child cope within a school context, by giving them the support they need. It very very often becomes completely irrelevant once school is out of the frame.
Don't let this agency's existence put you off home educating.
You write your dereg letter.
When the council or these Babcock people get in touch with you, you say "thank you so much for being in touch. In line with the Guidelines for Home Education 2007" (wrong title, but you'll find the pdf googling) we prefer to keep all communications with you in writing rather than having a visit"
They will write back and say "what is happening in the education, hmm? hmm?"
You write back and say "in accordance with the EHE Guidelines, we are taking a period of time for our daughter to deschool and settle into home education, in particular because of the trauma she has suffered within the school environment. We will be in touch in 3 months with further information about the education provision".
Over those three months, get comfortable with how your child begins to flourish out of school, see where her interests are and how they are developing. Then send them an educational philosophy "our educational approach is... we believe in..." so it's not specifics, it's your explanation of what your approach to your daughter's education is. " we think curriculums are really important, so we are following NC" or "we think it is really important that she comes out of this a confidence and independent learner so we are doing XYZ to facilitate that" whatever it is. usually about a side of A4. Then it is worth documenting some of the educational activities you have been doing, maybe categorised into academic areas (PSE, PE, literacy, numeracy, whatever is suitable to her age and stage). THen say "we intend to continue in this vein, while responding to our child's changing needs over the next year".
That's it. Don't give hostages to fortune "we will do 14 GCSEs by next Thursday" because that gives them something to judge you against.
If they want to see you, keep throwing the law back at them, unless they have reason to suppose there is a genuine welfare concern, in which case it is a matter for you to resolve with social services. There is no reason in law for anyone calling themselves any sort of home education officer or education welfare officer to be given access to your home or your child unless you want them to (and there is absolutely nothing in it for you or your child - local home educators are the ones who know how to home educate, not a bunch of council employees!)