Thamesmead's schools are among the best things about it. Nine in ten of the graded schools in its borough are good or better. Not one is rated inadequate. For most homes the nearest primary is a short walk. Thamesmead was built for families, and the part built for the children is the part that works.
Ofsted has graded 40 schools across the Royal Borough of Greenwich, and 37 of them are good or outstanding, so almost all of them. Eleven are outstanding, 26 good and three require improvement, and none is inadequate. Another 38 settings in Greenwich have no published grade yet, which is a gap in the inspection calendar and says nothing about how they are doing. These counts cover the whole of Greenwich, from the riverside estates out to the other end of the borough, so they describe the borough's schools as a group and give no single school's grade.
There is a complication particular to Thamesmead. It straddles Greenwich and Bexley, and the Ofsted counts above are Greenwich's alone. Places are allocated under each council's published admissions rules, so living near a school does not secure a place there, and which council runs your admissions depends on which side of the borough line your house is on. Find that out first, because the school down the road may be in the other borough and run under a different set of rules. Parents who learn about the border from an offer letter usually remember it.
The primaries are close. On the Department for Transport's 2019 model, the nearest primary is about seven minutes from the average home on foot, and about the same by public transport or car. Bishop John Robinson Church of England Primary School, a voluntary-aided school with a nursery on Hoveton Road, is named after a Bishop of Woolwich. Windrush Thamesmead Primary School carries the place's name, and Linton Mead Primary School is in the local mix as well. With primaries this close, the school run is the one journey in Thamesmead that never involves a bus.
Secondary school is further away. The same 2019 model puts the nearest secondary about 19 minutes away on foot, 15 minutes by public transport and nine by car, although bus timetables may have changed since then. Woolwich Polytechnic School and Woolwich Polytechnic School for Girls are both in Thamesmead, which gives families a boys' school and a girls' school without crossing the area. Both schools are named after Woolwich and are based in Thamesmead, an arrangement anyone used to the place's way with names will have stopped noticing.
On schools, Thamesmead does best by families of all its subjects, and the main question is which council's admissions rules your address falls under.