Before answering the the question, let us talk about how adverbs are used after verbs. In British English, adverbs are used independently after verbs without the help of prepositions. For example,
Come to school.
In the first example, ‘here’ is an adverb. So, no preposition is used after the verb ‘come’. But in the second example, since school is not an adverb, preposition ‘to’ is used after the verb. When intransitive verbs are extended, we need either an adverb or a prepositional phrase that works as adverbial.
Home is a word that can be used as noun, adjective, verb and adverb. After verbs of movement (e.g. come, go, run), we do not normally use ‘to’ before adverbs of place (e.g. here there, inside, home).
He goes home every week.
He comes home on Friday.
It was a nice day and so I decided to walk home.
If ‘home’ and the verb is separated by other words, ‘to’ is certainly used.
He went to his own home.