Very odd. I've looked up the legislation to which they refer, here: www.legislation.gov.uk/ukpga/2002/32/section/175
"175 Duties of LEAs and governing bodies in relation to welfare of children
(1)A local education authority shall make arrangements for ensuring that the functions conferred on them in their capacity as a local education authority are exercised with a view to safeguarding and promoting the welfare of children."
This is just a general principle guiding the LA's conduct in carrying out their usual duties. I don't understand how they can have "served you with a notice" under this legislation.
Did they threaten you with a School Attendance Order in their letter? If so, they've made a copy-and-paste error and quoted the wrong legislation to support their request for info. However, you should still respond promptly so as to fend off any possible prosecution. I don't agree with ommmward that the LA can't issue a School Attendance Order at this early stage. They shouldn't go straight to an SAO: it is considered bad practice. The 2007 government guidance to LAs regarding home education tells them not to - see below. But that doesn't mean they can't. Some LAs deliberately ignore the guidance, and some are just hopelessly incompetent.
("3.16 If a local authority considers that a suitable education is not being provided, then a full written report of the findings should be made and copied to the parents promptly, specifying the grounds for concern and any reasons for concluding that provision is unsuitable. If the authority is not satisfied that a suitable education is being provided, and the parents, having been given a reasonable opportunity to address the identified concerns and report back to the authority have not done so, the authority should consider sending a formal notice to the parents under section 437 (see paragraph 2.7) before moving on, if needed, to the issuing of a school attendance order (section 437(1)).")
I suggest you write back quickly by recorded delivery to ask for clarification. Something like this:
"Thank you for your letter of [date] regarding the education of my child [name]. I confirm that I am still home educating him.
For your reference, I enclose an additional copy of the education plan which I sent you on [date]. I understand you have a duty to act if it appears to you that my child is not receiving an adequate education. If this is the case, please write to me explaining what evidence leads you believe that I am not educating him suitably, and I will be glad to provide you with further information."
They can ask you for the moon if they want, in terms of detailed information about the child's education, frequent meetings at your home etc etc. But there is no legal basis for it. You've already given them some information. Unless they have something which causes them to think otherwise (e.g. neighbour accusing you of putting child to work in a sweatshop), they should assume all is well.
IMO the main principle now is to keep a dialogue going so they can't conclude you are ignoring them and that they need to escalate matters. Either just give them what they want, or else challenge why they need it.