A very interesting question. I shall deal with it in two parts:
Was he 'kidnapped'?
No. The definition of kidnapping only applies where someone is removed without their consent. Since this isn't is the case, the likely offence is one of "child abduction" per the Child Abduction Act (1984)
A person ... commits an offence if, without lawful authority or
reasonable excuse, he takes or detains a child under the age of
sixteen so as to remove him from the lawful control of any person
having lawful control of the child.
Although you could argue kidnap on the grounds of substantial coercion and that the child was not of sufficient age to consent, Harry's clear choice is to go to Hogwarts. Such a charge would not be supportable.
‘Er – I need to be at King’s Cross tomorrow to – to go to Hogwarts.’
Uncle Vernon grunted again.
‘Would it be all right if you gave me a lift?’
Was he 'abducted'?
A toughie. Certainly Hogwarts could be seen to have coerced his guardians by threats, including sending their resident half-giant around to the Dursley's house to smash up the place and injure their only natural-born child.
On the other hand, there was a sizeable gap between Hagrid's arrival and Harry leaving for school in which his guardians didn't simply do nothing to prevent any further risk of his going away but actually contributed to his leaving, including dropping him off (unsupervised) at the train station:
‘Barking,’ said Uncle Vernon, ‘howling mad, the lot of them. You’ll
see. You just wait. All right, we’ll take you to King’s Cross. We’re
going up to London tomorrow anyway, or I wouldn’t bother.’
‘Why are you going to London?’ Harry asked, trying to keep things friendly.
‘Taking Dudley to hospital,’ growled Uncle Vernon. ‘Got to have that
ruddy tail removed before he goes to Smeltings.’
This gives Hogwarts four strong defenses in their favour;
- It was the well-known choice of his parents that he went to Hogwarts:
His name’s been down ever since he was born.
His present guardians appear to have tacitly agreed to his leaving.
His present guardians are largely unfit. This would negate the primary defence that Hogwarts was not a fit person/institution to take action to remove him from the family:
‘I heard you went to live with Muggles,’ said Ron. ‘What are they
like?’ ‘Horrible – well, not all of them. My aunt and uncle and cousin
- Hogwarts (and the wizarding world in general) appears to be a separate jurisdiction in UK Law. It's at least arguable that Harry is considered a 'resident alien' in the UK which would give the wizgamot or Ministry of Magic some say over whether or not Hogwarts was a fit guardian in loco parentis