This proves to me that you don't know what you're talking about.
I'm from London. I spent every waking moment playing football and trained with a pro club called Brentford. My brother (who's better than me) trained with Chelsea, Brentford and Fulham and even he ended up playing semi-pro for a couple years.
Every single kid in the UK grows up having dreams of playing pro.
Every kid, no exeptions. Thats a lot of potential players for these clubs to pick from. And even if you do end up signing schoolboy terms with a top pro club, you still may not make it to the first team; you may not physically develop how they wanted you to, you may get seriously injured, or (and most commonly) you'll be usurped by a older, better, foregin player, and have to leave the club to a club lower down in the pyramid in order to play.
And 7 is early enough. Probably
too early. Players are usually brought into clubs at around 9-12 years of age.