Another idea..

Prior to the digital age, correspondence was often by public telephone. Is that what he was doing on the walks home from school?

Maybe he didn’t take the iPhone charger as he was going to meet someone who already had one…most likely a young person, perhaps a friend from the Lancaster event living in the south of England, not necessarily in London. The Pizza Hut sighting is a red herring. A lone 14 year old would surely eat in a more casual fast food joint such as McDonalds. The idea of him staying with family friends is also a red herring, if this was the case he would have taken at least a couple of days supply of clothes.(and his charger).

But why go on a school day?

Because something caused him to flee..