Dr Aswani at the Allum Centre in Leytonstone is excellent, but I don't know if you'll be close enough to their catchment area - it will probably depend on where in Walthamstow you are and whether you can plausibly claim a family connection to anyone who's already on their list.
The NHS website says "Leyton/Leytonstone" for their catchment. I live on Hoe Street about 1200 metres north of Boundary Road; it's not impossible that it's in the area, but I I doubt it. Worth checking though - I asked on Twitter and that's the only recommendation I got there, as well.
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