This letter shows far better awareness of the law and of their responsibilities than most LAs' letters. I would still take issue with the claim that "Department for Education guidelines encourage Local Authorities to make informal enquiries regarding the education which home educating parents provide in order that they may satisfy themselves that this is a full-time education suitable to a child's age, ability, aptitude and any special needs he/she may have." Unless there is some guidance from DfE which I haven't seen, this is not the case.
In fact, the 2007 EHE Guidelines for Local Authorities issued by the then-DCSF stated that
"2.7 Local authorities have no statutory duties in relation to monitoring the quality of home education on a routine basis.
However, under Section 437(1) of the Education Act 1996, local authorities shall intervene if it appears that parents are not providing a suitable education." (Emphasis is as shown in the original document.)
LAs sometimes claim that the subsequent Children Missing Education legislation places a positive duty on LAs to attempt to satisfy themselves that a suitable education is taking place whenever they are aware of the existence of any HE child, and not just in cases where it appears that parents are not providing a suitable education. However, the CME legislation refers back to the EHE guidelines and directs LAs to carry out their duties in compliance with the EHE guidelines, so it is clear that those guidelines have not been overridden.
Some of the more militant HE parents point this out to their LA and refuse to supply any details of their child's education unless and until the LA can demonstrate good reason why it appears to them that a suitable education is not taking place. (An LA's statement that "we don't know whether it is or not" isn't the same as an appearance that a suitable education isn't taking place!) Although I personally do take this militant line, I should say that I believe the vast majority of HE parents don't choose to do so, preferring to submit information in response to routine enquiries.
If you feel it is best to comply with your LA's request then I agree with previous posters: an educational philosophy with some examples would be good.