Okay, the LA staff are trying to mislead you into believing that they have powers which they don't have. They have no right to require a meeting. The government's 2007 guidance to LAs regarding how they should deal with home ed families, which is still in force, states this specifically in simple language, so there is no excuse for their little game. It's a useful document which is well worth a read: www.gov.uk/government/publications/elective-home-education
As you'll see from the above document, it is also quite dodgy for them to ask how many hours per week you are educating your child, as this presupposes a school-style formal education occurring during certain hours, with no learning happening outside those times, which is fairly ridiculous in a home ed situation. (Would anyone expect you to answer the question of how many hours per week you spend parenting your child?) So this is another indication that the person in post is either completely untrained in even the most basic elements of HE and the law, or knows quite well what they are doing and are trying to impose their own agenda on you.
Letters from the LA should always be answered, even if it is only to challenge the basis of what they are asking of you. If you ignore them entirely, they may start legal proceedings against you, which is a hassle you can do without. There are various options open to you.
You could comply with their demands. I'd advise against this fairly strongly, especially in your case. You would be allowing someone who is either clueless or manipulative into your home to make subjective judgements about what they find there and create a report based on their interpretations. It's true that you could get lucky and find the person perfectly lovely, but why take a chance? If you want a lovely supportive knowledgeable person to visit your home and give you advice, you can very likely find such a person in your local HE community... with no strings attached.
The middle ground which leaves you on very firm footing is this. Write them a report describing the education you are providing, outlining your general approach and listing both formal and informal learning opportunities. It doesn't have to be very lengthy; a few sides of A4 should be plenty. If your son has only just come out of school then the LA should give you a few months to settle in, so you could start off by writing a brief letter now saying that you don't require a visit and telling them the date by which you will send them a report.
A more confrontational approach is this. You could quote the law to them, observing that they are only required to intervene in elective home education if they have reason to believe a suitable education isn't being provided, and challenge them to tell you what basis they have for believing this. (By analogy, you probably wouldn't be happy to invite the police in for a rummage round your house just to demonstrate that you have no stolen property lying around, when they have no particular reason to believe that you do. You might turn them away on principle even though you have nothing to hide.) This approach tends to be followed by the more politically-minded, as it can involve some back-and-forth with letters and can take more time than simply stumping up a report right away.