Tiptop
I live in the countryside with my DC's.
After school, DS 12 plays in the woods with his friends. Catches fish, builds dens, rope swings, chops wood, gets utterly filthy. He bike rides through the countryside 'geo-catching'. He comes home to a hot meal, a bath and family time. We help with homework and nurture hobbies.
That's what I call an 'immersive experience'. If London does not suit family life. Move.
A family friend sent her 3 children to boarding school a few years back. She changed, the DC's were at best dismissive/ambivalent and full of distain when they were at home. I am not saying this to be nasty OP, honest. I am aware others who board will enjoy they experience. For me, it's a huge gamble and as crass as this will sound, sending children to boarding school is off-sourcing parenting.
Another parent I knew was adamant she wanted her kids to be privately educated, so she moved home so they could 'Day-Board', which involved coming home most nights, with the option to stay over once or twice a week if there were extra activities.