Hi, I also work at Kings and live in Herne Hill. It's a 20 minute walk and my eldest son is in reception at Bessemer Grange, we turned down our Dulwich infants offer as we were so impressed with Bessemer! It's a lovely school and Herne Hill is a wonderful community to live in, we have been here for 7 years. There are trains from North Dulwich to London Bridge or Herne Hill station to Victoria. Good luck with your searches!