You should look in areas on the Overground East London Line, as Ginster mentioned - As well as Peckham Rye and Denmark Hill, look at Brockley, Forest Hill, Honor Oak, Sydenham, Penge and Crystal Palace. There are a lot of budget supermarkets like Lidl, Aldi and Iceland. Other supermarkets like Waitrose, Sainsbury, Asda and Tesco all do home delivery, and that includes Iceland. There are car clubs here to rent a car for use if you don?t have one at first. Look into the use of Oyster cards on Transport for London on the TFL website - Transport for London. www.tfl.gov.uk