The schools are the strongest part of Woolwich's case. Nearly every graded school in the borough is good or better. About a quarter of them are outstanding. None is rated inadequate. A primary is a few minutes' walk from most front doors.
Across the Royal Borough of Greenwich, Ofsted has graded 40 schools, and 37 of them are good or better. That is nearly all of them. Eleven are outstanding, 26 good and 3 require improvement, and none is inadequate. Another 38 settings in the borough have no published overall grade yet, so they are left out of those counts. On a local authority list this long, three schools needing improvement is a short tail.
Distance is the easy part. The Department for Transport's modelled 2019 journey times put the nearest primary about six minutes' walk from the average Woolwich home, and the nearest secondary about 14 minutes on foot or by public transport. The council allocates places under its published admissions rules, so being close to a school helps but does not decide who gets in, and a short walk to the gate is no promise of a place. The rules can mean different things for faith schools, all-through schools and academies, even when they share a street.
A few schools say something about the area. Saint Mary Magdalene Church of England All Through School takes children from primary age through to secondary, which removes the anxious move at eleven for families who get in at the start. Plumstead Manor School and Ark Greenwich Free School are the other secondaries in the list, and Shooters Hill Sixth Form College takes students after sixteen. Mulgrave Primary School and St Margaret's Church of England Primary School are among about twenty primaries in and around Woolwich and Plumstead, and Waterside School is one of the specialist settings. Some schools that once served the area, including a primary and a secondary, have closed. An old map or an old listing can still send a family towards a building that is no longer a school.
If a particular school matters, get the Royal Borough of Greenwich's admissions rules for that school and see how places were allocated in recent years before you commit to a street. In the end the allocation rules decide, so check them yourself.
Woolwich families get a better choice of schools than the rest of the town's numbers would lead them to expect, and the schools are the best thing it offers them.