If you are under 65 you will have great difficulty in finding a local home as these are virtually non existence If you are of pension age - consider The Elms in Barry Road.
Why not consider an extra care sheltered housing unit which are available for those 55 and over. Carers being on the premises. If you are a private/council tenant you may be considered for Lew Evans House in ED or Lime Tree House in Nunhead. Also new SHU is opening in Commercial Way.
McCarthy and Stone are amongst private companies who have retirement properties with care on site - the nearest that I know of is in Catford.