hi
private:
I think the private primary school gatehouse school by Victoria park runs a school bus to wapping, but you should check with them. Parents are happy with them, but they're a typical 'mid range' private school - i.e. not at the top end, just somewhere upper middle class people send their kids. Small-ish class sizes.
Other nearby private options where you'll need to take children to school yourself from wapping are Faraday School at trinity buoy warf, The Lyceum school in Shoreditch and St Paul's Cathedral school. Further afield some kids go to all-through schools like Blackheath High school. Parents we know are happy with all of those - but worth visiting yourself.
public:
The better schools in/near wapping are: St Peter's London Docks, English Martyrs and The Aldgate School in the City of London. Hermitage school is also ok but usually a 2nd/3rd choice.
St Peters, English Martyrs and The Aldgate School select on religious observance - e.g. kid needs to be christened/baptised, and attend the right church for 2 years, signing the register each week and then get a letter from the priest.
Some people have been lucky and got their child into the school without doing this if there's a low-birthrate year. Some times spots open up in classes during the year as people move etc. But they're more often over subscribed.
Always worth applying though as there are moves before school year starts.
Plenty of parents pretend to be religious to get their kids in then stop going to church. Or just get the kid baptised and cross their fingers that it's enough.
There are also some flats/houses right next door to the schools and you might squeeze in one of the handful of non-religious places if you live super close.
All 3 of those school are great, have their own strengths etc. But again, best to visit and see how you feel, how transport will work for you and so on.