there's a huge back story, Cat64
As the law currently stands, the police only have the power to enter your home if there is "probable cause" - ie, if they have reason to suppose that you are breaking or have broken the law in some way, and if they have a warrant. Social workers only have the power to enter a private home, similarly, if they have reason to suppose that a child is being or is in imminent danger of being harmed.
Here we have a family about whom noone has any reason to suppose they are committing a crime, and an employee of the LA trying to intimidate them into consenting to an intrusion into the privacy of their home. That LA employee does not have a leg to stand on, legally. And the family has absolutely nothing to gain from inviting the LA person in. He has nothing to offer them - no funding, no free swimming lessons, no access to school libraries. Why on earth would a family want to meet with him? there is no carrot, and the stick has no legal power.
At present, parents are responsible for ensuring that their children are receiving an education; the LA can make enquiries in order to satisfy themself that an education is taking place, but nowhere in the law are they given the power to demand that those enquiries take place face to face.
The child is not missing from their family, their friends or community. They are only missing from some database, and that is the problem of the database owners, not of the family. It's a big civil liberties issue, Cat64, and home educators have been somewhat in the thick of it since January, when the government announced an inquiry into whether HE is being used as a cover for abuse. The review author concluded that although he had no evidence that this is a problem, it would be a good idea to legislate as though HEers are all child abusers, and subject us to intrusive inspections and a scheme whereby we would have to apply for permission, annually, to HE our children, with permission being granted or denied at the whim of the LA. (they are calling it registration, but it is in fact licensing). It is creating a huge stink - including a select committee enquiry (yet to report) and, only this week, a record number of petitions presented by MPs to parliament on the issue - something like 120 on a single day, mostly with the relevant MPs there putting them into the box behind the speaker's chair, and a few where one person submitted petitions for a couple of constituencies. It's a massive clash between government and governed, with thousands of people campaigning against any change to the law, and the conservatives having decided, thank God, to support us. We are all hoping that labour run out of parliamentary time before the bill goes through. It would fundamentally reshape the relationship between the state and the family, and not in a good way.