On paper, Fulham's schools are about as good as a set of schools gets. Every graded school in the borough came out good or outstanding at its last inspection, and twelve of them got the top grade. None has been told it needs to improve. The primaries and secondaries both post solid results. In Fulham the hard part is getting a place, and the quality mostly takes care of itself.
There are 11 mainstream state primaries in the area, and their pupils' average Key Stage 2 maths score is about 108. Fulham Primary School is the one with the place's name on it. St John's Walham Green Church of England Primary School still uses the name the tube station gave up when Walham Green became Fulham Broadway, so at least one institution round here held out against the rebranding.
The area has 6 mainstream state secondaries, and their pupil-weighted Attainment 8 score is about 59. The Hurlingham Academy and The London Oratory School are among them, and the other four give families real choice at eleven, along with a long kitchen-table argument about it.
Ofsted has graded 28 schools and settings across the whole Hammersmith and Fulham authority, and every one came out good or outstanding: 12 outstanding, 16 good, and none rated requires improvement or inadequate. Another 24 settings across the borough have no published grade yet and are outside those counts. Stamford Bridge, down the Fulham Road, would be glad of a clean sheet that tidy.
Places are allocated under Hammersmith and Fulham's published admissions rules, so buying near a named school does not on its own put a child in it. Look up the admissions criteria for the specific school you have in mind while the purchase is still at an early stage. Parents who assume a short walk means a seat sometimes find out in spring that the council read the rules more closely than they did.
Schools are where Fulham is hardest to fault. The competition is for places, and the standard holds up wherever a child ends up.