Hi
There is an assumption there anybody paid for any schooling or that indeed he attended a school at all. Board school and a concept of education for all at its most elementary, is still some way away at the time of the 1840s. He may have got some schooling through the church on Sundays. Did he sign his name on his marriage? He certainly learnt a trade so he experienced some sort of apprenticeship, but that may have been paid for by the poor law union if he entered the workhouse as indeed he might have received some elementary schooling from that source.
The known missing pieces for the 1841 census are these
HO107/668 covering St Luke, West Finsbury, Golden-Lane, Old Street and Whitecross-Street
HO107/680 covering Paddington
HO107/690 covering part of Kensington, Brompton and part of Kensal Green
If his father had died his mother may very well be working as a servant somewhere in London and he may be boarded with a family so not necessarily together and not necessarily in Wapping, where if she had family, she might have returned when she was too ill to work. It is at that point he may have been absorbed into part of the extended family or entered into the local poor law union. If so the union would decide on whatever trade they could find for the child and apprentice them out as soon as possible (then they would no longer be chargeable to the rates) - 7 would be a standard age.
Regards
Valda